the AJAX engine sends an HTTP request
There isn't really an Ajax engine there. It is the browser who initiates a request. Normally to initiate a request a user must perform some action - enter an address in the browser and hit enter, refresh the page, click a link on a page, submit a form. That will lead to the browser replacing the page with a new one, whatever comes as a result of the request.
Typically partial Ajax requests are used to obtain some partial information to update a portion of the page. But you can come up with any scenario you want.
that's how you can find out on the server what kind of request it was (if you need). You could serve a partial response to an Ajax request and a full page to a full request.
P.S. The technique is usually written as Ajax (only the first letter is capitalized). The notation of AJAX has become associated with the Microsoft ASP.NET AJAX library.