botch vs mistake

botch and mistake both are nouns.

Word	Noun	Adjective	Verb	Adverb
botch	Yes	No	Yes	No
mistake	Yes	No	Yes	No

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

botch: an embarrassing mistake
mistake: a wrong action attributable to bad judgment or ignorance or inattention

Other hypernyms of botch include error, fault.

botch (noun)	mistake (noun)
an embarrassing mistake	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

botch (verb)	mistake (verb)
make a mess of, destroy or ruin	to make a mistake or be incorrect
	identify incorrectly