Address review nits

compiler/rustc_lint/messages.ftl

@@ -6,7 +6,7 @@ lint_array_into_iter =
         or use `IntoIterator::into_iter(..)` instead of `.into_iter()` to explicitly iterate by value
 
 lint_async_fn_in_trait = use of `async fn` in public traits is discouraged as auto trait bounds cannot be specified
-    .note = you can suppress this lint if you plan to use the trait locally, for concrete types, or do not care about auto traits like `Send` on the `Future`
+    .note = you can suppress this lint if you plan to use the trait only in your own code, or do not care about auto traits like `Send` on the `Future`
     .suggestion = you can alternatively desugar to a normal `fn` that returns `impl Future` and add any desired bounds such as `Send`
 
 lint_atomic_ordering_fence = memory fences cannot have `Relaxed` ordering

compiler/rustc_lint/src/async_fn_in_trait.rs

@@ -39,8 +39,8 @@ declare_lint! {
     /// }
     ///
     /// fn test<T: Trait>(x: T) {
-    ///     fn is_send<T: Send>(_: T) {}
-    ///     is_send(x.method()); // Not OK.
+    ///     fn spawn<T: Send>(_: T) {}
+    ///     spawn(x.method()); // Not OK.
     /// }
     /// ```
     ///
@@ -68,11 +68,10 @@ declare_lint! {
     /// }
     /// ```
     ///
-    /// Conversely, if the trait is used only locally, if only concrete types
-    /// that implement the trait are used, or if the trait author otherwise
-    /// does not care that the trait will not promise that the returned
-    /// [`Future`] implements any [auto traits] such as [`Send`], then the
-    /// lint may be suppressed.
+    /// Conversely, if the trait is used only locally, if it is never used in
+    /// generic functions, or if it is only used in single-threaded contexts
+    /// that do not care whether the returned [`Future`] implements [auto traits]
+    /// such as [`Send`], then the lint may be suppressed.
     ///
     /// [`Future`]: https://doc.rust-lang.org/core/future/trait.Future.html
     /// [`Send`]: https://doc.rust-lang.org/core/marker/trait.Send.html

tests/ui/async-await/in-trait/warn.stderr

@@ -4,7 +4,7 @@ error: use of `async fn` in public traits is discouraged as auto trait bounds ca
 LL |     async fn not_send();
    |     ^^^^^
    |
-   = note: you can suppress this lint if you plan to use the trait locally, for concrete types, or do not care about auto traits like `Send` on the `Future`
+   = note: you can suppress this lint if you plan to use the trait only in your own code, or do not care about auto traits like `Send` on the `Future`
 note: the lint level is defined here
   --> $DIR/warn.rs:4:9
    |