Use success() or complete() in AJAX call

Question

Is it that success() returns earlier than complete()?

Yes; the AJAX success() method runs before the complete() method.

Below is a diagram illustrating the process flow:

AJAX call process flow diagram.

It is important to note that

The success() (Local Event) is only called if the request was successful (no errors from the server, no errors with the data).
On the other hand, the complete() (Local Event) is called regardless of if the request was successful, or not. You will always receive a complete callback, even for synchronous requests.

… more details on AJAX Events here.