People tend to use the words interchangeably but the two mean very different things:
To barbecue means to cook a meat over a low temperature of 225 to 250 degrees Fahrenheit (107 to 121 Celsius) for several hours (you might hear this referred to as "low and slow"). This method creates a tender meat that falls off the bone. It's mainly used for tough cuts like pork shoulder and brisket that require long cooking times to break down the collagen and melt the fat. Smoking and barbecuing are technically the same thing, though we tend to use the term "smoking" for chicken and fish more than for pork.
Grilling, on the other hand, is hot and fast. It's best for lean cuts of meat like steaks and chicken breasts. These don't require long cook times and should be grilled very quickly at a temperature of 350 degrees F (177 C) or hotter [sources: Southern Living, Raichlen].
There are two kinds of grilling, direct and indirect:
Direct grilling means cooking the meat at a very high heat over the fire — 600 degrees F (315 C). The high heat sears the meat and seal in the juices. It's used for small cuts of meat (steak, shrimp or kebabs) and the fire is usually left uncovered.
Indirect grilling is a hybrid between barbecuing and grilling. The temperature is high — around 350 degrees F — and the meat is cooked off to the side of the coals or heat source, as opposed to directly over it. This method allows your grill to function more like an oven and get some of that barbecue tenderness but in less time. It is best for whole chickens, rib roasts and other large fatty meats. Not every grill allows you to do indirect grilling [source: Raichlen].