To go a step further, broiling is a method of cooking whereby the heat source is above the food. Heat is transfered to the food solely by infra-red radiation rather than by convection or conduction. TEmperature control is obtained by controlling the temperature of the heat source, and by moving the food closer or further away from the heat source.
Broiling is usually done on a pan which is designed to allow grease to fall away and into a contained space. This elliminates popping grease and ignition of that grease into flame. Broiling is used where a dry, high heat is required to sear and caramelize the food surface by the time the center is heated sufficiently.
Grilling is a technique where the heat source is located under the food. It is essentially the same as broiling, but produces the famous "Grilled" flavor as the hot crease drips onto the heat source (charcoal, ceramic bricks, or metallic baffles) and produces smoke which deposits itself onto the food. Again, the heat is transfered to the food by intense infra-red radiation. Because grilling produces substantial amounts of smoke, most stoves and ovens don't have grills built into them. You would seriously smoke up you house. Of course there are models like the Jen-Air stoves with down draft ventillation systems that will draw sufficient air into them to elliminate the smoke from your home. And those large, flat heating surfaces called grills in restaurant kitchens are really just giant skillets without sides. They cook by conduction.
And that, my freind, is the difference between grillilng and broiling. Oh, and hte heat source can be electrick coils, or a gas flame for either. But I don't think you will find a charcoal boiler. You'd end up with such a mess of ashes.
Seeeeeeya; Goodweed of the North