Are you interested in girls? Do you like girls? I don't see much of a difference here. If you are interested in something, as in you take an interest in it, then that means that you like that thing. But when it comes to studying something, if you study something you like, then that is about all there is to it. If you study something you are interested in, maybe this implies you want to delve (dig, go more deeply into) the subject. And maybe if you go further into a subjectm you will discover that you will don't like it, or don't like it as much as you thought you did.

The difference is very small, but I would say "something you like" is emotional while "something you are interested in" is intellectual.