These three words are loosely ranked as to how much they count toward your grade. In order of importance, they are (from least to most important): quiz, test and exam. A test and exam may mean the same thing. When I got my final "test" for my degree, I was given an oral exam. It was very important in determining whether I got my degree or not. I was nervous. I wouldn't have been nearly as nervous about a quiz. A test would have been somewhere in between, as far as effort and importance.

QUIZ is quite shorter (and sometimes extemporaneous) while TEST is longer. An EXAM usually comes at the end of let's say, semester and covers the whole course's most important and pretty complex points. Among these three, of course, EXAM is where we exert much preparation time. :)

A quiz is usually a game played for fun, there are lots of quiz programmes on TV. A test can be an exam but also you can have an eye test, a blood test or driving test. The term 'exam' is usually used in academic subjects.

I gave thumbs up to Maxey but mostly because Romulus used the word extemporaneous. Test and exam can mean the same. A quiz is the annoying things teachers give to see if you understood a point.