What is the purpose of the rivet set and snap?

A rivet set is a tool used to seat the rivet while drawing the material to be joined together to eliminate any voids or spaces between the head of the rivet and the materials to be joined. Some rivet sets also have an indentation to assist in both initially deforming the rivet to "set it" and to assist in the final shaping, though in days of old the tool that was used for the final shape of a rivet was also sometimes referred to as a snap. But in another time a snap was what a round head rivet was called. This all, of course, was just to add a bit of generational confusion.