It is govenment that matters with "учить" and "учиться". I mean, HOW you use the verb.
УЧИТЬ кого-то чему-то = to teach someone(Acc) someting(Dat)
УЧИТЬ что-то = to learn/study/try to memorize something (Acc) → isn't used in the meaning "study something scientifically/doing research"
then you have reflexive учиться:
УЧИТЬСЯ чему-то / делать что-то = to learn something (Dat)/ to learn to do something
УЧИТЬСЯ = to be engaged in the activity of learning something → "to study"
УЧИТЬСЯ где-то = to attend some educational facility. You can specify a) school/university/course/faculty b) year ("в третьем классе", "на втором курсе")
ИЗУЧАТЬ что-то = to study something (Acc) → also means, more specifically, attending a formal academic program or studying something scientifically/doing research. Self-study is also an option (though, I would prefer "учить" in informal context)
ЗАНИМАТЬСЯ чем-то = lit. "to be occupied with" → to engage in the activity of something(Ins). Sometimes learning/mastering something in a repeated activity, especially when the activity is something you'd likely to learn (languages, swimming). Заниматься спортом, though, is just about activity.
ЗАНИМАТЬСЯ = to study (in general). Think of sitting at your desk or lying in bed with textbooks, or audio materials etc. "To be in a prolonged state of studying, putting effort to learn things".