In the old days, it seems Firefox was based on xulrunner, but newer releases seem to be independent of that module.
If I'm going to study the Firefox source code, should I still take a look at the xulrunner?
XULRunner is basically a platform that allows you to run XUL applications. As you probably know, addons for Firefox and Thunderbird are actually XUL applications. You can run Chatzilla independently of Firefox by using XULRunner, for example.
The relationship between XULRunner and Firefox is that Firefox could probably be described as a XULRunner/Gecko package. XULRunner does the work of the XUL applications, whereas Gecko does the rendering.
Depending on what you want to achieve by studying the Firefox source code, you may not need to be familiar with XULRunner at all.