What type? It's a sandwich. A bun with a meat patty as a filling. It's the evolution of the Hamburg Steak which was evolution of Steak Tartar. Steak Tartar is seasoned raw beef minced, Hamburg Steak is steak tartar that has been molded together and cooked, the hamburger is a Hamburg Steak on a bun.
...ideally. Few people remember the origins and forget to season the hamburger.