Await Vs Task.Wait - Deadlock?

Answer :

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.

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.