Broil, Grill, and Roast

To say the conclusion, I am still confused the clear meaning, though.. I found a new word: Broil. It means to cook meat or fish under direct heat or over heat on metal bars. The word is chosen by the U.S. However, the British use Grill in the same situation instead. I got interested in these words, so, I studied the difference between these words: Broil, Grill, and Roast.

Grill means very similar to Broil, but they have lots of difference like the picture I attached. One of the points, the heat source of Grill is always below, while, the heating source of Broil is above or below. Both grilling and broiling involve intense direct heat, though.
Roast has a different usage, the meaning is to cook food, especially meat by prolonged exposure to heat in an oven or over a fire from a long distance.

I have checked these words with some dictionaries and web pages, but I have still not made sense of the difference, even though I took an hour to investigate. I will ask a person who lives in the U.S. about it. Thank you!