I guess there are cases when these words are interchangeable. Research, however seems to be more scientific. It has to do with looking things up, finding something, etc. Let me try to give an example:
When you do research on a book, you must know all the relevant things that others have written about it -to study it, it may be enough to read the book alone.
When you study a language, you might simply learn that language, maybe read some of the famous literature, etc., when you do research, you are more likely to collect data on the usage, etc.