Fangirls tend to obsess over people/fandoms that are very much in the popular culture spotlight; geeks tend to seek out the more obscure fandoms. For example, there are very few fangirls for Vladimir Nabokov.

Those who love Lord of the Rings for the mythos and the languages tend to be geeks; those who love the movie actors tend to be fangirls. Sometimes the two camps, no matter the amount of overlap, do get into minor territorial wars; the geeks who loved LotR prior to movies were probably upset about the massive influx of new fans (some of which were geek-material who had simply never heard of LotR before, like me, but most of which were fangirls) and may even have bordered on the, "But you can't like it for that! We were here first!"