What's the difference between returning void and returning a Task?

SLaks and Killercam's answers are good; I thought I'd just add a bit more context.

Your first question is essentially about what methods can be marked async.

A method marked as async can return void, Task or Task<T>. What are the differences between them?

A Task<T> returning async method can be awaited, and when the task completes it will proffer up a T.

A Task returning async method can be awaited, and when the task completes, the continuation of the task is scheduled to run.

A void returning async method cannot be awaited; it is a "fire and forget" method. It does work asynchronously, and you have no way of telling when it is done. This is more than a little bit weird; as SLaks says, normally you would only do that when making an asynchronous event handler. The event fires, the handler executes; no one is going to "await" the task returned by the event handler because event handlers do not return tasks, and even if they did, what code would use the Task for something? It's usually not user code that transfers control to the handler in the first place.

Your second question, in a comment, is essentially about what can be awaited:

What kinds of methods can be awaited? Can a void-returning method be awaited?

No, a void-returning method cannot be awaited. The compiler translates await M() into a call to M().GetAwaiter(), where GetAwaiter might be an instance method or an extension method. The value awaited has to be one for which you can get an awaiter; clearly a void-returning method does not produce a value from which you can get an awaiter.

Task-returning methods can produce awaitable values. We anticipate that third parties will want to create their own implementations of Task-like objects that can be awaited, and you will be able to await them. However, you will not be allowed to declare async methods that return anything but void, Task or Task<T>.

(UPDATE: My last sentence there may be falsified by a future version of C#; there is a proposal to allow return types other than task types for async methods.)

(UPDATE: The feature mentioned above made it in to C# 7.)

In case the caller wants to wait on the task or add a continuation.

In fact, the only reason to return void is if you cannot return Task because you're writing an event handler.

Methods returning Task and Task<T> are composable - meaning that you can await them inside of an async method.

async methods returning void are not composable, but they do have two other important properties:

1. They can be used as event handlers.
2. They represent a "top-level" asynchronous operation.

The second point is important when you're dealing with a context that maintains a count of outstanding asynchronous operations.

The ASP.NET context is one such context; if you use async Task methods without awaiting them from an async void method, then the ASP.NET request will be completed too early.

Another context is the AsyncContext I wrote for unit testing (available here) - the AsyncContext.Run method tracks the outstanding operation count and returns when it's zero.