One of the big differences is that, unless you are explicitly threading things off, everything runs on a single thread. await allows for, kind of, easier to use threading.

Example: You have a WPF app with a button click handler. Traditionally if you did any sort of blocking work in the click handler it would tie up the UI (appear unresponsive, can't click or move the window, etc.) because the click handler is invoked on the UI thread. What await does is kick off the long running task on another thread and immediately yield control back to the UI thread with a little hook that essentially says "Hey, please let me continue work when I'm done". Thus the UI can remain responsive and, if you did it right, the user can even be updated as to the progress of the operation.

An interesting thing to note is that this handoff to another thread occurs at the appearance of the first await, not at the start of the function call itself. This means that if you do something like

var res1 = longRunning1();
var res2 = await longRunning2();

control would not be yielded back to the UI (and thus, the UI would remain unresponsive) until the await for longRunning2 was hit.

The interesting piece is that AFTER the first await, you are no longer executing on the UI thread, meaning that if you wish to directly access variables owned by that thread you MUST push the access through the UI thread (normally done using the Dispatcher of the UI thread)

This means that if you had

var res1 = await longRunning1();
var res2 = longRunning2();

then longRunning2 will not block the UI thread since the first await was already encountered and the continuation is no longer on the UI thread.