I'm resurrecting this thread but I think this needs some clarification. People tend to use these terms indiscriminately, but where I come from (the southern part of the U.S.) there is a clear distinction. Barbecue is cooked very slowly on very low heat and over coals or wood chips (someone gas). This infuses the meat with intense flavors and helps to keep it tender and moist. Grilling is what most people do when they slap some hotdogs and hamburgers on the grill, cooking it quickly over high heat. You can also grill fruits and vegetables. Barbecue is ideal for tougher cuts of meat. In the South, when someone invites you to a barbecue, it means that you are actually going to eat barbecued meat such as baby-back ribs, pulled pork, brisket, or chicken. Now that I live in the North, I notice that people here use barbecue, even when there's nothing but maybe some hamburgers, hot dogs, and chicken on the grill (I've been had twice like this). In the South, we'd call this a cookout.
As for the shrimp, shrimp is grilled because you can't cook it too long unless you want it have a rubbery tasty. If you see barbecue(d) shrimp, it just means that the it was grilled and that perhaps barbecue sauce was spread on top.