In Montana, barbeque means anything cooked on a grill. You barbeque hamburgers, steak, chicken, whatever. If you cook on the grill, you're having a barbeque.
When I moved to FloriDUH, I quickly learned that barbeque there is meat that is simmered in sauce, or meat that is simmered/braised/smoked or what have you and then smothered in sauce. If you cook on the grill in FL, you're having a cookout.