There are two meanings of which I know.
For example, next Saturday (the 16th), a bunch of us are going to a restaurant to have food of the "barbecue" variety. This means things like ribs and such with the appropriate smoky flavor and requisite sauces placed upon them.
Three weeks after that, we're having a big barbecue at our new house (for the out-of-town bloggers who will be attending GB:NYC-2 that weekend, as well as the disreputable group of New Yorkers we refer to as our friends). ;) This time, "barbecue" means I will load charcoal into the Weber grill, pour 12 gallons of lighter fluid on it (because what's the fun if the flames don't threaten passing aircraft?) and light her up.
I'll let the coals get nice and hot, and then I'll "barbecue" hamburgers, hot dogs and various other items of food.
I suppose the ribs, etc., type of barbecue has some involvement with cooking over coal, but that's where the similarities seem to end, so what's the deal? Which one is barbecue and which one isn't? The restaurant we're going to is called Tennessee Mountain Barbecue. So do people in Tennessee also cook hamburgers over charcoal fires? This is all so terribly confusing!