I do not think there is such thing different type of research papers. In my opinion, research paper is a research paper. Topic and style can be different, but research paper itself is a type of academic writing. I remember somebody here asked what type of research paper takes a position on the topic. The answer was rather apparent - argumentative or persuasive type of writing.
Of course, if you wonder what type of research papers are there, you may want to talk to your teacher about that. I am sure you can also contact any online essay writing service with the same question and puzzle them with your request about types.