Grilling and broiling both use intense direct heat to cook foods. They both require the same watchful eye to avoid burning. And they both provide a similar charring and caramelization that give food that distinct flavor. However, grills and broilers work differently to achieve these goals.
The biggest difference between a grill and an oven broiler is that your oven as a thermostat to control temperature. While this might seem like it would simplify the process the problem is that your oven can turn off then it gets to a certain temperature (about 500 to 550 degrees F.(260 to 288 degrees C.)). This will leave foods to cook in their own steam. Something you don't want then grilling. You want that constant direct heat. To keep your broiler burning, prop open the door. This allows heat to escape and will keep the oven from reaching its highest temperature. This will keep foods from baking and it keeps the burner burning.
Like grilling you want the grease and fat to be able to drip away, therefore you always want to use a broiling pan. And like a grill you want to preheat the surface that is going to be in contact with the food so preheat the broiler pan. Since you are cooking by direct heat you don't have to worry about preheating the oven itself. The hot pan, however will help you get good searing on the surface of meats. Unless you are cooking something very thin you might still need to flip it half way through the cooking process to get it even.
Like grilling you need to keep a close eye while broiling. Foods can still easily burn and even catch fire. Keep a fire resistant mitt close by and stay close to the oven while broiling. An instance read thermometer is also a very good thing to have on hand. Broiling might take longer than grilling because the temperatures might not be as high, but don't assume that it will take longer.
The one big difference with your broiler is that the smoke it makes is inside you home and not rising out of the backyard. While keeping a close eye on your broiling will help prevent burning and smoke, you should consider avoiding as much fat as possible with those items you broil. This means trimming excess fat from meats, but it also means cutting back on oil-based marinades. Also avoid overcooking foods to reduce the amount of smoke.
While broiling won't give foods the same great grilled flavor, in a pinch it can be a very good way to cook. Pay attention to what you are doing and you will quickly master the differences with grilling.