There are three basic mantels;

Shelf mantel: A shelf mantel is a free standing shelf mounted on a wall. A shelf mantel stands alone and does not have any legs.
Full surround: A full surround mantel is what people typically envision when thinking of a mantel. It consists of a top shelf, breast board and legs. Though a mantel can be plain, it is usually decorated with crown mouldings, panel moulds and other details.

Cap Mantel: A cap mantel is a shelf mantel that is made to overlap the top of the fireplace. The bottom of the cap mantel is hollow so as to allow it to cover a masonry projection.