Translation:What is this movie about?
I don't have a dictionary definition, but for me they carry different connotations. 关于 means "about" in the more strict sense. "What is this movie about?" On the other hand, 为 has more of a purpose oriented idea. I think it's closer to "for" than "about". The phrase 这是为了什么? translates to "what is this for?" rather than "what is this about?"