A full brisket can be classified as a “Packer Brisket”. This means it contains both main muscles the point and the flat. Rarely do I hear of people smoking just the “point” but you can find the “flat” at grocery stores. That can be good for pickling and making corn beef.
The brisket point and flat confused me when I started barbecue. I always got them mixed up. Flat means just what it sounds like, it’s flat. The brisket kind of forms a point and that is what always confused me but the flat part or the part that is slim is considered the Flat. The hump or part that seems a little meatier is the Point. Both are great when it comes to brisket. Typically the flat is known for being a little leaner. The Point is known for being a little fattier. Neither are wrong choices and both have their benefits. For pictures, I like showing off the flat, but to eat I am more of a point kind of guy.