I don't really understand the difference. Understand you'd say:

"я учусь в московском университете."
я изучаю Физику or any subject.

And it appears that заниматься is talking about actual studying. As in reading the book actually in the process of study. I think I understand this one.

What I don't understand is учиться vs. изучать.

Is изучать used when talking about subjects only? And учиться when talking about schools? I really don't get it.