diff --git a/Cargo.toml b/Cargo.toml
index 6612b1630986e..560ae5807f43c 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -872,12 +872,12 @@ category = "ECS (Entity Component System)"
 wasm = false
 
 [[example]]
-name = "system_chaining"
-path = "examples/ecs/system_chaining.rs"
+name = "system_piping"
+path = "examples/ecs/system_piping.rs"
 
-[package.metadata.example.system_chaining]
-name = "System Chaining"
-description = "Chain two systems together, specifying a return type in a system (such as `Result`)"
+[package.metadata.example.system_piping]
+name = "System Piping"
+description = "Pipe the output of one system into a second, allowing you to handle any errors gracefully"
 category = "ECS (Entity Component System)"
 wasm = false
 
diff --git a/crates/bevy_ecs/src/lib.rs b/crates/bevy_ecs/src/lib.rs
index 6143036737dbb..90fd426e43d72 100644
--- a/crates/bevy_ecs/src/lib.rs
+++ b/crates/bevy_ecs/src/lib.rs
@@ -38,7 +38,7 @@ pub mod prelude {
             Schedule, Stage, StageLabel, State, SystemLabel, SystemSet, SystemStage,
         },
         system::{
-            adapter as system_adapter, Commands, In, IntoChainSystem, IntoSystem, Local, NonSend,
+            adapter as system_adapter, Commands, In, IntoPipeSystem, IntoSystem, Local, NonSend,
             NonSendMut, ParallelCommands, ParamSet, Query, RemovedComponents, Res, ResMut,
             Resource, System, SystemParamFunction,
         },
diff --git a/crates/bevy_ecs/src/schedule/state.rs b/crates/bevy_ecs/src/schedule/state.rs
index 3037500b6caa6..3ad5dbef5f059 100644
--- a/crates/bevy_ecs/src/schedule/state.rs
+++ b/crates/bevy_ecs/src/schedule/state.rs
@@ -3,7 +3,7 @@ use crate::{
         RunCriteriaDescriptor, RunCriteriaDescriptorCoercion, RunCriteriaLabel, ShouldRun,
         SystemSet,
     },
-    system::{In, IntoChainSystem, Local, Res, ResMut, Resource},
+    system::{In, IntoPipeSystem, Local, Res, ResMut, Resource},
 };
 use std::{
     any::TypeId,
@@ -79,7 +79,7 @@ where
         (move |state: Res<State<T>>| {
             state.stack.last().unwrap() == &pred && state.transition.is_none()
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
@@ -95,7 +95,7 @@ where
             Some(_) => false,
             None => *is_inactive,
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
@@ -118,7 +118,7 @@ where
             Some(_) => false,
             None => *is_in_stack,
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
@@ -133,7 +133,7 @@ where
                     _ => false,
                 })
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
@@ -148,7 +148,7 @@ where
                     _ => false,
                 })
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
@@ -162,7 +162,7 @@ where
                     _ => false,
                 })
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
@@ -176,7 +176,7 @@ where
                     _ => false,
                 })
         })
-        .chain(should_run_adapter::<T>)
+        .pipe(should_run_adapter::<T>)
         .after(DriverLabel::of::<T>())
     }
 
diff --git a/crates/bevy_ecs/src/system/function_system.rs b/crates/bevy_ecs/src/system/function_system.rs
index 5cbaa6d88c379..c3f672e718734 100644
--- a/crates/bevy_ecs/src/system/function_system.rs
+++ b/crates/bevy_ecs/src/system/function_system.rs
@@ -499,7 +499,7 @@ impl<T> Copy for SystemTypeIdLabel<T> {}
 ///
 /// # Example
 ///
-/// To create something like [`ChainSystem`], but in entirely safe code.
+/// To create something like [`PipeSystem`], but in entirely safe code.
 ///
 /// ```rust
 /// use std::num::ParseIntError;
@@ -510,8 +510,8 @@ impl<T> Copy for SystemTypeIdLabel<T> {}
 /// // Unfortunately, we need all of these generics. `A` is the first system, with its
 /// // parameters and marker type required for coherence. `B` is the second system, and
 /// // the other generics are for the input/output types of `A` and `B`.
-/// /// Chain creates a new system which calls `a`, then calls `b` with the output of `a`
-/// pub fn chain<AIn, Shared, BOut, A, AParam, AMarker, B, BParam, BMarker>(
+/// /// Pipe creates a new system which calls `a`, then calls `b` with the output of `a`
+/// pub fn pipe<AIn, Shared, BOut, A, AParam, AMarker, B, BParam, BMarker>(
 ///     mut a: A,
 ///     mut b: B,
 /// ) -> impl FnMut(In<AIn>, ParamSet<(SystemParamItem<AParam>, SystemParamItem<BParam>)>) -> BOut
@@ -529,15 +529,15 @@ impl<T> Copy for SystemTypeIdLabel<T> {}
 ///     }
 /// }
 ///
-/// // Usage example for `chain`:
+/// // Usage example for `pipe`:
 /// fn main() {
 ///     let mut world = World::default();
 ///     world.insert_resource(Message("42".to_string()));
 ///
-///     // chain the `parse_message_system`'s output into the `filter_system`s input
-///     let mut chained_system = IntoSystem::into_system(chain(parse_message, filter));
-///     chained_system.initialize(&mut world);
-///     assert_eq!(chained_system.run((), &mut world), Some(42));
+///     // pipe the `parse_message_system`'s output into the `filter_system`s input
+///     let mut piped_system = IntoSystem::into_system(pipe(parse_message, filter));
+///     piped_system.initialize(&mut world);
+///     assert_eq!(piped_system.run((), &mut world), Some(42));
 /// }
 ///
 /// #[derive(Resource)]
@@ -551,7 +551,7 @@ impl<T> Copy for SystemTypeIdLabel<T> {}
 ///     result.ok().filter(|&n| n < 100)
 /// }
 /// ```
-/// [`ChainSystem`]: crate::system::ChainSystem
+/// [`PipeSystem`]: crate::system::PipeSystem
 /// [`ParamSet`]: crate::system::ParamSet
 pub trait SystemParamFunction<In, Out, Param: SystemParam, Marker>: Send + Sync + 'static {
     fn run(&mut self, input: In, param_value: SystemParamItem<Param>) -> Out;
diff --git a/crates/bevy_ecs/src/system/mod.rs b/crates/bevy_ecs/src/system/mod.rs
index bb177a279ac2e..2243636e3182f 100644
--- a/crates/bevy_ecs/src/system/mod.rs
+++ b/crates/bevy_ecs/src/system/mod.rs
@@ -75,8 +75,8 @@ mod function_system;
 mod query;
 #[allow(clippy::module_inception)]
 mod system;
-mod system_chaining;
 mod system_param;
+mod system_piping;
 
 pub use commands::*;
 pub use exclusive_function_system::*;
@@ -84,8 +84,8 @@ pub use exclusive_system_param::*;
 pub use function_system::*;
 pub use query::*;
 pub use system::*;
-pub use system_chaining::*;
 pub use system_param::*;
+pub use system_piping::*;
 
 /// Ensure that a given function is a system
 ///
diff --git a/crates/bevy_ecs/src/system/system_chaining.rs b/crates/bevy_ecs/src/system/system_piping.rs
similarity index 79%
rename from crates/bevy_ecs/src/system/system_chaining.rs
rename to crates/bevy_ecs/src/system/system_piping.rs
index 17e0c0455bc39..4f4a192ff535d 100644
--- a/crates/bevy_ecs/src/system/system_chaining.rs
+++ b/crates/bevy_ecs/src/system/system_piping.rs
@@ -7,10 +7,11 @@ use crate::{
 };
 use std::borrow::Cow;
 
-/// A [`System`] that chains two systems together, creating a new system that routes the output of
-/// the first system into the input of the second system, yielding the output of the second system.
+/// A [`System`] created by piping the output of the first system into the input of the second.
 ///
-/// Given two systems `A` and `B`, A may be chained with `B` as `A.chain(B)` if the output type of `A` is
+/// This can be repeated indefinitely, but system pipes cannot branch: the output is consumed by the receiving system.
+///
+/// Given two systems `A` and `B`, A may be piped into `B` as `A.pipe(B)` if the output type of `A` is
 /// equal to the input type of `B`.
 ///
 /// Note that for [`FunctionSystem`](crate::system::FunctionSystem)s the output is the return value
@@ -28,10 +29,10 @@ use std::borrow::Cow;
 ///     let mut world = World::default();
 ///     world.insert_resource(Message("42".to_string()));
 ///
-///     // chain the `parse_message_system`'s output into the `filter_system`s input
-///     let mut chained_system = parse_message_system.chain(filter_system);
-///     chained_system.initialize(&mut world);
-///     assert_eq!(chained_system.run((), &mut world), Some(42));
+///     // pipe the `parse_message_system`'s output into the `filter_system`s input
+///     let mut piped_system = parse_message_system.pipe(filter_system);
+///     piped_system.initialize(&mut world);
+///     assert_eq!(piped_system.run((), &mut world), Some(42));
 /// }
 ///
 /// #[derive(Resource)]
@@ -45,7 +46,7 @@ use std::borrow::Cow;
 ///     result.ok().filter(|&n| n < 100)
 /// }
 /// ```
-pub struct ChainSystem<SystemA, SystemB> {
+pub struct PipeSystem<SystemA, SystemB> {
     system_a: SystemA,
     system_b: SystemB,
     name: Cow<'static, str>,
@@ -53,7 +54,7 @@ pub struct ChainSystem<SystemA, SystemB> {
     archetype_component_access: Access<ArchetypeComponentId>,
 }
 
-impl<SystemA: System, SystemB: System<In = SystemA::Out>> System for ChainSystem<SystemA, SystemB> {
+impl<SystemA: System, SystemB: System<In = SystemA::Out>> System for PipeSystem<SystemA, SystemB> {
     type In = SystemA::In;
     type Out = SystemB::Out;
 
@@ -121,33 +122,34 @@ impl<SystemA: System, SystemB: System<In = SystemA::Out>> System for ChainSystem
     }
 }
 
-/// An extension trait providing the [`IntoChainSystem::chain`] method for convenient [`System`]
-/// chaining.
+/// An extension trait providing the [`IntoPipeSystem::pipe`] method to pass input from one system into the next.
+///
+/// The first system must have return type `T`
+/// and the second system must have [`In<T>`](crate::system::In) as its first system parameter.
 ///
-/// This trait is blanket implemented for all system pairs that fulfill the chaining requirement.
+/// This trait is blanket implemented for all system pairs that fulfill the type requirements.
 ///
-/// See [`ChainSystem`].
-pub trait IntoChainSystem<ParamA, Payload, SystemB, ParamB, Out>:
+/// See [`PipeSystem`].
+pub trait IntoPipeSystem<ParamA, Payload, SystemB, ParamB, Out>:
     IntoSystem<(), Payload, ParamA> + Sized
 where
     SystemB: IntoSystem<Payload, Out, ParamB>,
 {
-    /// Chain this system `A` with another system `B` creating a new system that feeds system A's
-    /// output into system `B`, returning the output of system `B`.
-    fn chain(self, system: SystemB) -> ChainSystem<Self::System, SystemB::System>;
+    /// Pass the output of this system `A` into a second system `B`, creating a new compound system.
+    fn pipe(self, system: SystemB) -> PipeSystem<Self::System, SystemB::System>;
 }
 
 impl<SystemA, ParamA, Payload, SystemB, ParamB, Out>
-    IntoChainSystem<ParamA, Payload, SystemB, ParamB, Out> for SystemA
+    IntoPipeSystem<ParamA, Payload, SystemB, ParamB, Out> for SystemA
 where
     SystemA: IntoSystem<(), Payload, ParamA>,
     SystemB: IntoSystem<Payload, Out, ParamB>,
 {
-    fn chain(self, system: SystemB) -> ChainSystem<SystemA::System, SystemB::System> {
+    fn pipe(self, system: SystemB) -> PipeSystem<SystemA::System, SystemB::System> {
         let system_a = IntoSystem::into_system(self);
         let system_b = IntoSystem::into_system(system);
-        ChainSystem {
-            name: Cow::Owned(format!("Chain({}, {})", system_a.name(), system_b.name())),
+        PipeSystem {
+            name: Cow::Owned(format!("Pipe({}, {})", system_a.name(), system_b.name())),
             system_a,
             system_b,
             archetype_component_access: Default::default(),
@@ -156,7 +158,7 @@ where
     }
 }
 
-/// A collection of common adapters for [chaining](super::ChainSystem) the result of a system.
+/// A collection of common adapters for [piping](super::PipeSystem) the result of a system.
 pub mod adapter {
     use crate::system::In;
     use std::fmt::Debug;
@@ -168,9 +170,9 @@ pub mod adapter {
     /// use bevy_ecs::prelude::*;
     ///
     /// return1
-    ///     .chain(system_adapter::new(u32::try_from))
-    ///     .chain(system_adapter::unwrap)
-    ///     .chain(print);
+    ///     .pipe(system_adapter::new(u32::try_from))
+    ///     .pipe(system_adapter::unwrap)
+    ///     .pipe(print);
     ///
     /// fn return1() -> u64 { 1 }
     /// fn print(In(x): In<impl std::fmt::Debug>) {
@@ -204,7 +206,7 @@ pub mod adapter {
     ///     .add_system_to_stage(
     ///         CoreStage::Update,
     ///         // Panic if the load system returns an error.
-    ///         load_save_system.chain(system_adapter::unwrap)
+    ///         load_save_system.pipe(system_adapter::unwrap)
     ///     )
     ///     // ...
     /// #   ;
@@ -224,7 +226,7 @@ pub mod adapter {
         res.unwrap()
     }
 
-    /// System adapter that ignores the output of the previous system in a chain.
+    /// System adapter that ignores the output of the previous system in a pipe.
     /// This is useful for fallible systems that should simply return early in case of an `Err`/`None`.
     ///
     /// # Examples
@@ -248,7 +250,7 @@ pub mod adapter {
     ///     .add_system_to_stage(
     ///         CoreStage::Update,
     ///         // If the system fails, just move on and try again next frame.
-    ///         fallible_system.chain(system_adapter::ignore)
+    ///         fallible_system.pipe(system_adapter::ignore)
     ///     )
     ///     // ...
     /// #   ;
@@ -278,8 +280,8 @@ pub mod adapter {
             unimplemented!()
         }
 
-        assert_is_system(returning::<Result<u32, std::io::Error>>.chain(unwrap));
-        assert_is_system(returning::<Option<()>>.chain(ignore));
-        assert_is_system(returning::<&str>.chain(new(u64::from_str)).chain(unwrap));
+        assert_is_system(returning::<Result<u32, std::io::Error>>.pipe(unwrap));
+        assert_is_system(returning::<Option<()>>.pipe(ignore));
+        assert_is_system(returning::<&str>.pipe(new(u64::from_str)).pipe(unwrap));
     }
 }
diff --git a/examples/README.md b/examples/README.md
index 18853ac19db1a..4e105d66d9ee3 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -199,9 +199,9 @@ Example | Description
 [Removal Detection](../examples/ecs/removal_detection.rs) | Query for entities that had a specific component removed in a previous stage during the current frame
 [Startup System](../examples/ecs/startup_system.rs) | Demonstrates a startup system (one that runs once when the app starts up)
 [State](../examples/ecs/state.rs) | Illustrates how to use States to control transitioning from a Menu state to an InGame state
-[System Chaining](../examples/ecs/system_chaining.rs) | Chain two systems together, specifying a return type in a system (such as `Result`)
 [System Closure](../examples/ecs/system_closure.rs) | Show how to use closures as systems, and how to configure `Local` variables by capturing external state
 [System Parameter](../examples/ecs/system_param.rs) | Illustrates creating custom system parameters with `SystemParam`
+[System Piping](../examples/ecs/system_piping.rs) | Pipe the output of one system into a second, allowing you to handle any errors gracefully
 [System Sets](../examples/ecs/system_sets.rs) | Shows `SystemSet` use along with run criterion
 [Timers](../examples/ecs/timers.rs) | Illustrates ticking `Timer` resources inside systems and handling their state
 
diff --git a/examples/ecs/system_chaining.rs b/examples/ecs/system_piping.rs
similarity index 85%
rename from examples/ecs/system_chaining.rs
rename to examples/ecs/system_piping.rs
index 8046dcd7ec3d1..ca023ab7afef3 100644
--- a/examples/ecs/system_chaining.rs
+++ b/examples/ecs/system_piping.rs
@@ -1,5 +1,5 @@
-//! Illustrates how to make a single system from multiple functions running in sequence and sharing
-//! their inputs and outputs.
+//! Illustrates how to make a single system from multiple functions running in sequence,
+//! passing the output of the first into the input of the next.
 
 use anyhow::Result;
 use bevy::prelude::*;
@@ -7,7 +7,7 @@ use bevy::prelude::*;
 fn main() {
     App::new()
         .insert_resource(Message("42".to_string()))
-        .add_system(parse_message_system.chain(handler_system))
+        .add_system(parse_message_system.pipe(handler_system))
         .run();
 }