.mov, .mkv, .avi and others are containers which mean they're like sandwiches, I tell clients. (Did you see that? I began a sentence with a period, hah! Mrs. Roberts was wrong!) Not all sandwiches are good, and asking me for "a quicktime" or "an mov" or "an avi" is like asking me for "a sandwich on white bread". You've specified that you want a sandwich (video file), with white bread (container format) but you have yet to tell me what kind of sandwich you want (codec).
This seems to be the only way to get through to some clients. "You're ordering a sandwich with white bread but I don't know what kind of sandwich you want. PB&J? Mustard and Lettuce? Cheese and Anchovies?" "What do you recommend?" is usually their response. I dunno. What kind of sandwich does the thingy that you're going to play it on ask for? In the manual. Yes, that one, the one you didn't read.
Today I literally said to a particularly ornery client, "I need to know what you want between the bread, otherwise we're going to have to try a bunch and see which works and looks good." See, I'm making a video in an outdated format, using outdated software for a client's outdated hardware. This is the kinda fun that only a college education can provide, kids.
Things like H.264 solve this problem. They're PB&J sandwiches all the time. And something known as a "standard".