IMO grilling and broiling are two VERY different things. As has been explained, grilling means direct heat underneath food placed on a grate, while broiling means direct heat above the food placed in a dish or on a tray.
Usually grilling is done on the open so the steam can escape, while broiling is done in a closed oven. Your results will be very different.
Also, when grilling, the melting fat from what you food will fall on the coals or the metal bars of your grill, and burn, creating smoke. That's true of both coal or gas grills. That smoke gives your food the "barbecue" taste. No such thing with a broiler.
Try grilling potatoes au gratin. Or a skinless buttery fish fillet such as Turbot or Black Cod. Good luck with that!

on the other hand... broiled hamburger anyone? Hmmmmm.... maybe not.