This should settle it (taken from foodnetwork.com):
"With your Hawaiian shirt-wearing neighbors milling around your deck during a Saturday afternoon barbecue, you toss chicken breasts on your barbecue's hot grill, slather them with some of that tangy barbecue sauce and yank them off 15 minutes later. You say you are barbecuing, but here you would be wrong."
"A barbecue can be a backyard event, a cooking appliance and a sauce. Principally, though, it's a process, and it's defined by two elements: smoke and time. What you were doing with those chicken breasts involved neither. You were grilling."
"To barbecue is to suspend meat over long-smoldering coals that broadcast smoke from hardwoods like hickory, oak, alder or cherry. To barbecue is to - in most cases - invest at least an hour in your masterpiece, and sometimes 12 hours or more. And to barbecue is to commune with an age-old American ceremony that nearly matches the diversity of the nation that hatched baseball, rock 'n' roll and Wall Street."