However, many of my friends from other regions consider BBQ a verb, IE; BBQing is the act of cooking BBQ (with fire), or grilling.
Back to the nouns...for my friends from Boston, BBQ is simply synonymous with grill. For other regional friends, BBQ is synonymous with cookout.
I think in a less enlightened time (ie, the dark ages when I was a kid) not many people knew about offset smoking at home, let alone pellets or whatnot. Having a cookout with the family and friends/neighbors was all there really was, so the name barbecue was applied both to the activity and to the resulting meat (usually hamburgers & hot dogs). All that was done over charcoal for the most part. The popularity of gas came a bit later.
I think it was about 30-40 years ago that I remember people starting to make a distinction between BBQ and "Grilling", the latter being over either charcoal or gas with direct heat. BBQ was low-and-slow cooking, indirect heat, and considered an advanced technique. About the same time, grilling anything other than steaks or the previously mentioned hamburgers and hot dogs started being more popular. Grilling was the "low fat way" to cook your meat and (a new emphasis) veggies.
What do *I* consider BBQ? I would say cooking over a grate, as compared to wet braising in a dutch oven or cooking on flattop/frying in a pan. So for me, that steak over the charcoals in your Weber is still BBQ. It's all a bit muddled though--wrapping your brisket in foil for a Texas crutch is essentially braising. Does it matter? No. Is it good eating? YUP!