OPEN. ABSOLUTELY:

Because broiling is supposed to be heating by radiant heat. In this process the surface is heated on the side exposed to the burner/coil, while the rest of the victim is surrounded by cooler (not exactly cool, but ...) air. This gives a nice crisp "skin" on the side facing the heat, but gives slow penetration of heat to the innards for a tender and juicy main body of the meat.

If you close the door (unless it's one of the new-fangled vented designs) all of the air in the oven heats up, and you're baking instead of broiling.

There's nothing wrong with either method, but to be pedantically correct, if the door is open¹ you're broiling; but if the door is shut you're baking with the top heater.

¹ The real dividing line would be that to broil you need a "heater" hot enugh to radiate (450-500F/230-260C usually works nicely), with surrounding air cool enough to avoid rapid heating of the core of the meat. Depending on what you're cooking, an air temp above about 140-160F (60-70C) may result in a noticeably tougher finished meal, especially with beef. Pork is usually a little less sensitive to rapid heating, and with some poultry it's hard to tell much difference.

Similar differences may be found with other cooking methods, although only the "real pro" is likely to be finicky about the distinctions.

e.g. "To sauté" really is not the same as to "fry," and stewing is different than parboiling (or steaming); although most people don't much care about the difference if they can stuff a dead critter someplace where there's heat to the meat.

John