Fastest is more likely to refer to top speed, and quickest is more likely to refer to the 0-60 times. But yes that's subjective difference in usage and not a strict definition.

Acceleration versus top speed. Quick to me refers to a period of time whereas fast refers only to a point of time.

Thanks for asking; I was very confused as well. I still don't find the difference between the two terms satisfying. I would rather them state acceleration or speed versus quick and fast.