XUL was defined to build the user interface of the Mozilla open source browser.

The name comes from a character of the Ghostbuster movie.

XUL provides user interface bases for a cross platform application. As DHTML was created for web page interface, XUL has been created for interface of applications.

XUL is a markup language to design graphical user interfaces, by using an XML subset created by Mozilla.
Ajax is the main component of Web applications and Web 2.0 sites, and provides a simple mean to interact with the server. Both Ajax and XUL are using JavaScript.   More detail...