fail vs botch

fail is not a noun while botch is a noun.

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

As verbs, botch is a hyponym of fail; that is, botch is a word with a more specific, narrower meaning than fail:

fail (noun)	botch (noun)
	an embarrassing mistake

fail (verb)	botch (verb)
stop operating or functioning	make a mess of, destroy or ruin
deteriorate
prove insufficient
disappoint, prove undependable to; abandon, forsake
become bankrupt or insolvent; fail financially and close
be unsuccessful
fail to get a passing grade
fail to do something; leave something undone
judge unacceptable
be unable
fall short in what is expected