*difference. Quick is a measure of time, fast is a measure of speed.

"Quick" applies particularly to something practically instantaneous, an action of very brief duration. "Fast" refers to actions that continue for a time, and usually to those that are uninterrupted.

Sometimes they can mean the same thing. A cheetah is fast. A cheetah is quick. However, 'fast' can refer to something which occurs at great speed over a long period of time. The jet plane is fast, traveling at 700 kph. Quick is used more to refer to something that happens in a short period of time. He quickly stepped out of the way to avoid being hit by the car. In a game of football (in U.S., soccer), you want forwards who are fast, but goalies who are quick. The forwards must run longer distances to get to the ball and try to score. The goalie does not have to cover a large distance, but needs to react quickly to block shots in the small space he defends.

And—to answer your original question—"fast" is an adjective (describing what kind of thing—car, plane, runner, etc.) and "quickly" is an adverb (describing how something moves/functions).

Fast is speed. Quick is acceleration. Hussein Bolt was the fastest in the olympics, but he was not the quickest (because he does not accelerate as fast as the others).