Gina - We call that chopped beef, and it's usually made from the leftovers after you trim and slice the brisket, but it is really good.
Of course, being from Texas, I have eaten plenty of BBQ, and it has nothing to do with hamburgers, steaks, or even a grill. It's made in a huge contraption, called a pit, usually made from oil drums, that you can pull behind your truck. It involves a brisket for sure, and sometimes other meats, including goat (yuck). They start cooking and drinking the night before, and the meat is good and ready by the next evening. The sauces are a mixture of all kinds of things, depending on the cook. "Cooking" and cutting the meat is generally male territory. The women simply purchase everything (except the pit because that's male bragging rights, the bigger the better and often exagerrated like the male anatomy), trim and season the meat, carry it out to the pit, remind the by then drunk men to check on, turn over, baste, and take off the meat, prepare all the side dishes, wash the dishes and clean up.