From Wikipedia.

Barbecue or barbeque[1] (abbreviated BBQ, Bar-B-Q or Bar-B-Que or diminuted, chiefly in Australia, New Zealand and the United Kingdom to barbie, and braai in South Africa) is a method and apparatus for cooking food, often meat, with the heat and hot gases of a fire, smoking wood, or hot coals of charcoal and may include application of a marinade, spice rub, or basting sauce to the meat. The term as a noun can refer to foods cooked by this method, to the cooker itself, or to a party that includes such food. The term is also used as a verb for the act of cooking food in this manner. Barbecue is usually cooked in an outdoor environment heated by the smoke of wood or charcoal, or with propane and similar gases. Restaurant barbecue may be cooked in large brick or metal ovens specially designed for that purpose.

Also of note:

In British English usage, barbecuing and grilling refer to a fast cooking process directly over high heat, whilst grilling also refers to cooking under a source of direct, high heat–known in the US and Canada as broiling. In US English usage, however, grilling refers to a fast process over high heat whilst barbecuing refers to a slow process using indirect heat and/or hot smoke. For example, in a typical US home ‘grill’, food is cooked on a grate directly over hot charcoal; while in a US ‘barbecue’, the coals are dispersed to the sides or at significant distance from the grate.

Obviously, if I say, “I’m BBQing in the back yard” and I’m using a grill with coals under it, I’m Barbequeing.

Also grilling, but still Barbequeing.

End of fucking story.