AJAX is a technological concept, not a specific implementation. Google uses AJAX but who knows what type of server they are running on. (Probably their own OS by now, last I knew they ran a massive Beowolf Linux cluster.) Microsoft has an AJAX framework for use in ASP.NET. There are also 3rd party implementations of AJAX frameworks.
It really comes down to this: javascript calls the web server using a client side object, typically the
XmlHttpRequest object (different browsers have different implementations of this). The server processes the request and send back some text (ironically, more often then not it's NOT XML). The response needs to be in a form that makes sense to the calling javascript (XML, JSON, etc). The javascript processes the response and performs some action on the document it's running in such as updating an HTML element.
-Peter