Async annotates a method so it is going to be called asynchronously.

@org.springframework.stereotype.Service
public class MyService {
    @org.springframework.scheduling.annotation.Async
    void DoSomeWork(String url) {
        [...]
    }
}

So Spring could do so you need to define how is going to be executed. For example:

<task:annotation-driven />
<task:executor id="executor" pool-size="5-10" queue-capacity="100"/>

This way when you call service.DoSomeWork("parameter") the call is put into the queue of the executor to be called asynchronously. This is useful for tasks that could be executed concurrently.

You could use Async to execute any kind of asynchronous task. If what you want is calling a task periodically you could use @Scheduled (and use task:scheduler instead of task:executor). They are simplified ways of calling java Runnables.

DeferredResult<> is used to answer to a petition without blocking the Tomcat HTTP thread used to answer. Usually is going to be the return value for a ResponseBody annotated method.

@org.springframework.stereotype.Controller
{
    private final java.util.concurrent.LinkedBlockingQueue<DeferredResult<String>> suspendedRequests = new java.util.concurrent.LinkedBlockingQueue<>();

    @RequestMapping(value = "/getValue")
    @ResponseBody
    DeferredResult<String> getValue() {
            final DeferredResult<String> result = new DeferredResult<>(null, null);
            this.suspendedRequests.add(result);
            result.onCompletion(new Runnable() {
            @Override
            public void run() {
        suspendedRequests.remove(result);
            }
});
            service.setValue(result); // Sets the value!
            return result;
    }
}

The previous example lacks one important thing and it's that doesn't show how the deferred result is going to be set. In some other method (probably the setValue method) there is going to be a result.setResult(value). After the call to setResult Spring is going to call the onCompletion procedure and return the answer to the HTTP request (see https://en.wikipedia.org/wiki/Push_technology#Long_polling).

But if you just are executing the setValue synchronously there is no advantage in using a deferred result.Here is where Async comes in hand. You could use an async method to set the return value in some point in the future using another thread.

    @org.springframework.scheduling.annotation.Async
    void SetValue(DeferredResult<String> result) {
        String value;
        // Do some time consuming actions
        [...]
        result.setResult(value);
    }

Async is not needed to use a deferred result, its just one way of doing it.

In the example there is a queue of deferred results that, for example, a scheduled task could be monitoring to process it's pending requests. Also you could use some non blocking mechanism (see http://en.wikipedia.org/wiki/New_I/O) to set the returning value.

To complete the picture you could search information about java standard futures (http://docs.oracle.com/javase/1.5.0/docs/api/java/util/concurrent/Future.html) and callables (http://docs.oracle.com/javase/1.5.0/docs/api/java/util/concurrent/Callable.html) that are somewhat equivalent to Spring DeferredResult and Async.