"Fast" and "quick". I think that these words are interchangeable when used as adjectives generally describing speed, but are less interchangeable ,or not at all interchangeable when used in adjectival phrases.
Adjectives
In their adjective forms, "fast" and "quick" are fairly similar ; look at their definitions.
fast adj. moving or able to move, operate, function, or take effect quickly; quick; swift; rapid
quick adj. done, proceeding, or occurring with promptness or rapidity, as an action, process
You can say:
The train is fast.
The train is quick.
Adjectival Phrases
While still being used as adjectives, "fast" and "quick" can have specific meanings when modifying certain words.
fast adj. characterized by unrestrained conduct or lack of moral conventions, esp. in sexual relations; wanton; loose
ex. Nancy is fast, as evidenced by her way of speaking and her cheap clothes.
fast adj. firm in adherence; loyal; devoted
ex. Joe and Chris were fast friends until the day they died.
quick adj. easily provoked or excited
ex. Your father has always been quick tempered.
quick adj. prompt to understand, learn, etc.; of ready intelligence:
ex. George is a quick student.