An analytical paper breaks down an issue or an idea into its component parts, evaluates the issue or idea, and presents this breakdown and evaluation to the audience.
An expository (explanatory) paper explains something to the audience.
An argumentative paper makes a claim about a topic and justifies this claim with specific evidence. The claim could be an opinion, a policy proposal, an evaluation, a cause-and-effect statement, or an interpretation. The goal of the argumentative paper is to convince the audience that the claim is true based on the evidence provided.