task: clarify doc about tasks starting immediately

tokio/src/runtime/handle.rs

@@ -118,9 +118,9 @@ impl Handle {
     /// thread pool. The thread pool is then responsible for polling the future
     /// until it completes.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the background
-    /// immediately when `spawn` is called.
+    /// The provided future will start running in the background immediately
+    /// when `spawn` is called, even if you don't await the returned
+    /// `JoinHandle`.
     ///
     /// See [module level][mod] documentation for more details.
     ///

tokio/src/runtime/runtime.rs

@@ -163,9 +163,9 @@ impl Runtime {
     /// thread pool. The thread pool is then responsible for polling the future
     /// until it completes.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the
-    /// background immediately when `spawn` is called.
+    /// The provided future will start running in the background immediately
+    /// when `spawn` is called, even if you don't await the returned
+    /// `JoinHandle`.
     ///
     /// See [module level][mod] documentation for more details.
     ///

tokio/src/runtime/task/join.rs

@@ -11,9 +11,9 @@ cfg_rt! {
     /// An owned permission to join on a task (await its termination).
     ///
     /// This can be thought of as the equivalent of [`std::thread::JoinHandle`]
-    /// for a Tokio task rather than a thread. You do not need to `.await` the
-    /// `JoinHandle` to make the task execute — it will start running in the
-    /// background immediately.
+    /// for a Tokio task rather than a thread. Note that the background task
+    /// associated with this `JoinHandle` started running immediately when you
+    /// called spawn, even if you have not yet awaited the `JoinHandle`.
     ///
     /// A `JoinHandle` *detaches* the associated task when it is dropped, which
     /// means that there is no longer any handle to the task, and no way to `join`

tokio/src/task/join_set.rs

@@ -120,9 +120,9 @@ impl<T: 'static> JoinSet<T> {
     /// Spawn the provided task on the `JoinSet`, returning an [`AbortHandle`]
     /// that can be used to remotely cancel the task.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the background
-    /// immediately when `spawn` is called.
+    /// The provided future will start running in the background immediately
+    /// when this method is called, even if you don't await anything on this
+    /// `JoinSet`.
     ///
     /// # Panics
     ///
@@ -143,9 +143,9 @@ impl<T: 'static> JoinSet<T> {
     /// `JoinSet` returning an [`AbortHandle`] that can be used to remotely
     /// cancel the task.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the background
-    /// immediately when `spawn_on` is called.
+    /// The provided future will start running in the background immediately
+    /// when this method is called, even if you don't await anything on this
+    /// `JoinSet`.
     ///
     /// [`AbortHandle`]: crate::task::AbortHandle
     #[track_caller]
@@ -162,9 +162,9 @@ impl<T: 'static> JoinSet<T> {
     /// `JoinSet`, returning an [`AbortHandle`] that can be used to remotely
     /// cancel the task.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the background
-    /// immediately when `spawn_local` is called.
+    /// The provided future will start running in the background immediately
+    /// when this method is called, even if you don't await anything on this
+    /// `JoinSet`.
     ///
     /// # Panics
     ///
@@ -186,10 +186,8 @@ impl<T: 'static> JoinSet<T> {
     /// remotely cancel the task.
     ///
     /// Unlike the [`spawn_local`] method, this method may be used to spawn local
-    /// tasks when the `LocalSet` is _not_ running. You do not have to `.await`
-    /// the returned `JoinHandle` to make the provided future start execution.
-    /// It will start running immediately whenever the `LocalSet` is next
-    /// started.
+    /// tasks on a `LocalSet` that is _not_ currently running. The provided
+    /// future will start running whenever the `LocalSet` is next started.
     ///
     /// [`LocalSet`]: crate::task::LocalSet
     /// [`AbortHandle`]: crate::task::AbortHandle

tokio/src/task/local.rs

@@ -289,9 +289,9 @@ cfg_rt! {
     ///
     /// The spawned future will run on the same thread that called `spawn_local`.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the background
-    /// immediately when `spawn_local` is called.
+    /// The provided future will start running in the background immediately
+    /// when `spawn_local` is called, even if you don't await the returned
+    /// `JoinHandle`.
     ///
     /// # Panics
     ///
@@ -417,10 +417,9 @@ impl LocalSet {
     /// This task is guaranteed to be run on the current thread.
     ///
     /// Unlike the free function [`spawn_local`], this method may be used to
-    /// spawn local tasks when the `LocalSet` is _not_ running. You do not have
-    /// to `.await` the returned `JoinHandle` to make the provided future start
-    /// execution. It will start running immediately whenever the `LocalSet` is
-    /// next started.
+    /// spawn local tasks when the `LocalSet` is _not_ running. The provided
+    /// future will start running once the `LocalSet` is next started, even if
+    /// you don't await the returned `JoinHandle`.
     ///
     /// # Examples
     ///

tokio/src/task/spawn.rs

@@ -7,9 +7,9 @@ cfg_rt! {
     /// Spawns a new asynchronous task, returning a
     /// [`JoinHandle`](super::JoinHandle) for it.
     ///
-    /// You do not have to `.await` the returned `JoinHandle` to make the
-    /// provided future start execution. It will start running in the background
-    /// immediately when `spawn` is called.
+    /// The provided future will start running in the background immediately
+    /// when `spawn` is called, even if you don't await the returned
+    /// `JoinHandle`.
     ///
     /// Spawning a task enables the task to execute concurrently to other tasks. The
     /// spawned task may execute on the current thread, or it may be sent to a