We usually use quick to refer to something happening in a short time, or a shorter than expected time: We stopped for a quick snack. Not: … a fast snack. I just need a quick answer. Not: … a fast answer. Fast refers to things that happen or go at high speed, e.g. a train, a person running: She loves fast cars. Not: She loves quick cars. Note the common expression fast food to refer to food such as hamburgers, which are cooked and served in a very short time in restaurants: You shouldn’t eat so much fast food. It’s not good for you.

a train may be fast, but it is never quick. Quick means fast buy also a rapid start. A grasshopper jump is very quick.

Lots of differences depending on the context, might be better to learn on a case-by-case basis... sorry! Just to note: 'fast' is used both as an adjective and adverb (he speaks so fast), whereas 'quick' is only ever an adjective - the adverb being 'quickly', of course. Might be useful to keep in mind!

As adjectives, these words have the same meaning - the opposite of 'slow'. There is no difference in meaning between the two words. In most cases they are interchangeable. However, when it comes to collocations (which words tend to be used together with other words), they are not always interchangeable. We say 'fast food', for example, but not 'quick food'. We'd also say 'I'll have a quick look at this' but not 'a fast look'.