mix-up vs mistake

mix-up and mistake both are nouns.

Word	Noun	Adjective	Verb	Adverb
mix-up	Yes	No	No	No
mistake	Yes	No	Yes	No

As nouns, mistake is a hypernym of mix-up; that is, mistake is a word with a broader meaning than mix-up:

mix-up: a mistake that results from taking one thing to be another
mistake: a wrong action attributable to bad judgment or ignorance or inattention

Other hypernyms of mix-up include error, fault.

mix-up (noun)	mistake (noun)
a mistake that results from taking one thing to be another	a wrong action attributable to bad judgment or ignorance or inattention
	an understanding of something that is not correct
	part of a statement that is not correct

mix-up (verb)	mistake (verb)
	to make a mistake or be incorrect
	identify incorrectly