await Task.Delay() vs. Task.Delay().Wait()

The second test has two nested tasks and you are waiting for the outermost one, to fix this you must use t.Result.Wait(). t.Result gets the inner task.

The second method is roughly equivalent of this:

public void TestAwait()
{
  var t = Task.Factory.StartNew(() =>
            {
                Console.WriteLine("Start");
                return Task.Factory.StartNew(() =>
                {
                    Task.Delay(5000).Wait(); Console.WriteLine("Done");
                });
            });
            t.Wait();
            Console.WriteLine("All done");
}

By calling t.Wait() you are waiting for outermost task which returns immediately.

The ultimately 'correct' way to handle this scenario is to forgo using Wait at all and just use await. Wait can cause deadlock issues once you attached a UI to your async code.

    [Test]
    public async Task TestCorrect() //note the return type of Task. This is required to get the async test 'waitable' by the framework
    {
        await Task.Factory.StartNew(async () =>
        {
            Console.WriteLine("Start");
            await Task.Delay(5000);
            Console.WriteLine("Done");
        }).Unwrap(); //Note the call to Unwrap. This automatically attempts to find the most Inner `Task` in the return type.
        Console.WriteLine("All done");
    }

Even better just use Task.Run to kick off your asynchronous operation:

    [TestMethod]
    public async Task TestCorrect()
    {
        await Task.Run(async () => //Task.Run automatically unwraps nested Task types!
        {
            Console.WriteLine("Start");
            await Task.Delay(5000);
            Console.WriteLine("Done");
        });
        Console.WriteLine("All done");
    }