The most obvious difference is that "faster" is a comparative form. The equivalent with "quick" would be "quicker." In most contexts, "fast" and "quick" are synonymous. But in the case of describing movements, "quick" often refers to the initial motion and "fast" refers to sustaining the motion. Other similar words include rapid, speedy, swift and brisk.

Re what word would you use when a friend is very slow hurry up , be quick or be faster thank you. Parents might sometimes say any of these: Stop dawdling! Get a move on! We haven't got all day. (All impatient) Come on slow coach! (More jovial). To adults / friends, you might say: Sorry, but we really need to get going. We need to get a move on otherwise we will be late.