differnce between compression test and leak down test?

I called a shop to get a price for a compression test. I told the mechanic that I was looking to see if I had any leaking seals, gaskets, etc. He told me that what I was really looking for is a leak down test. What exactly is the difference between the two and will the leak down tell me exactly what, if anything, is wrong with my engine?

a leak down test puts air into your engine to see where it will start leaking, also it ill sho up bubbles in the radiator if there are broken head gaskets, broken cylinder walls and more stuff.

a compression test just puts a gauge in place of your spark plug and they crank the engine at WOT. This method is used more to see if they use it to see if new rings are needed