diff --git a/spring-context/src/main/java/org/springframework/scheduling/concurrent/SimpleAsyncTaskScheduler.java b/spring-context/src/main/java/org/springframework/scheduling/concurrent/SimpleAsyncTaskScheduler.java
index 027d1f6f4f..d585470e4c 100644
--- a/spring-context/src/main/java/org/springframework/scheduling/concurrent/SimpleAsyncTaskScheduler.java
+++ b/spring-context/src/main/java/org/springframework/scheduling/concurrent/SimpleAsyncTaskScheduler.java
@@ -78,7 +78,9 @@ import org.springframework.util.ErrorHandler;
  * but rather just the hand-off to an execution thread.</b> As a consequence,
  * a {@link ScheduledFuture} handle (e.g. from {@link #schedule(Runnable, Instant)})
  * represents that hand-off rather than the actual completion of the provided task
- * (or series of repeated tasks).
+ * (or series of repeated tasks). Also, this scheduler participates in lifecycle
+ * management to a limited degree only, stopping trigger firing and fixed-delay
+ * task execution but not stopping the execution of handed-off tasks.
  *
  * <p>As an alternative to the built-in thread-per-task capability, this scheduler
  * can also be configured with a separate target executor for scheduled task
diff --git a/spring-core/src/main/java/org/springframework/core/task/SimpleAsyncTaskExecutor.java b/spring-core/src/main/java/org/springframework/core/task/SimpleAsyncTaskExecutor.java
index 4206695f0b..8412e6c4af 100644
--- a/spring-core/src/main/java/org/springframework/core/task/SimpleAsyncTaskExecutor.java
+++ b/spring-core/src/main/java/org/springframework/core/task/SimpleAsyncTaskExecutor.java
@@ -46,6 +46,11 @@ import org.springframework.util.concurrent.ListenableFutureTask;
  * executing a large number of short-lived tasks. Alternatively, on JDK 21,
  * consider setting {@link #setVirtualThreads} to {@code true}.
  *
+ * <p><b>NOTE: This executor does not participate in context-level lifecycle
+ * management.</b> Tasks on handed-off execution threads cannot be centrally
+ * stopped and restarted; if such tight lifecycle management is necessary,
+ * consider a common {@code ThreadPoolTaskExecutor} setup instead.
+ *
  * @author Juergen Hoeller
  * @since 2.0
  * @see #setVirtualThreads