Using wood or charcoal makes smoke and changes the flavor of the food. Using gas does not. Some people only like one type, and some people like both kinds of grilling.
The heat may be applied underneath the food, or above, or both. A barbecue is a typical machine for outdoor cooking using coke or other fuel for providing heat from underneath. Overhead grilling is more usual indoors, especially in professional kitchens.
In the United States there are cook-off grills, which are competitions. The most common meats used are steak, burgers and hot dogs. Grilling food is very common for holidays or celebrations like the 4th of July (United States Independence Day). Most people use a grill more outdoors in the summer time.