As a retired appliance salesguy, allow me my 2Cents.

Roasting and baking (in America) are basically the same process. It is called roasting for solid things as meats and potatoes; baking for liquid things, cakes, pies, breads. Those terms are occasionally interchangeable, I guess. In this process the food is air heated, and does not have contact with a direct flame. For roasting/baking the door must be closed, else the oven could not hold the proper cooking temperature.

Broiling, on the other hand, has the food place directly, usually under the flame or electric heat rods. Usually the food broiled is a meat. In gas broilers one usually has the door/drawer closed, but in electric oven/broilers the door is slightly ajar.