await vs Task.Wait - Deadlock?

Wait and await - while similar conceptually - are actually completely different.

Wait will synchronously block until the task completes. So the current thread is literally blocked waiting for the task to complete. As a general rule, you should use "async all the way down"; that is, don't block on async code. On my blog, I go into the details of how blocking in asynchronous code causes deadlock.

await will asynchronously wait until the task completes. This means the current method is "paused" (its state is captured) and the method returns an incomplete task to its caller. Later, when the await expression completes, the remainder of the method is scheduled as a continuation.

You also mentioned a "cooperative block", by which I assume you mean a task that you're Waiting on may execute on the waiting thread. There are situations where this can happen, but it's an optimization. There are many situations where it can't happen, like if the task is for another scheduler, or if it's already started or if it's a non-code task (such as in your code example: Wait cannot execute the Delay task inline because there's no code for it).

You may find my async / await intro helpful.

Some important facts were not given in other answers:

"async await" is more complex at CIL level and thus costs memory and CPU time.

Any task can be canceled if the waiting time is unacceptable.

In the case "async await" we do not have a handler for such a task to cancel it or monitoring it.

Using Task is more flexible then "async await".

Any sync functionality can by wrapped by async.

public async Task<ActionResult> DoAsync(long id) 
{ 
    return await Task.Run(() => { return DoSync(id); } ); 
} 

"async await" generate many problems. We do not now is await statement will be reached without runtime and context debugging. If first await not reached everything is blocked. Some times even await seems to be reached still everything is blocked:

https://github.com/dotnet/runtime/issues/36063

I do not see why I'm must live with the code duplication for sync and async method or using hacks.

Conclusion: Create Task manually and control them is much better. Handler to Task give more control. We can monitor Tasks and manage them:

https://github.com/lsmolinski/MonitoredQueueBackgroundWorkItem

Sorry for my english.

Based on what I read from different sources:

An await expression does not block the thread on which it is executing. Instead, it causes the compiler to sign up the rest of the async method as a continuation on the awaited task. Control then returns to the caller of the async method. When the task completes, it invokes its continuation, and execution of the async method resumes where it left off.

To wait for a single task to complete, you can call its Task.Wait method. A call to the Wait method blocks the calling thread until the single class instance has completed execution. The parameterless Wait() method is used to wait unconditionally until a task completes. The task simulates work by calling the Thread.Sleep method to sleep for two seconds.

This article is also a good read.