botch up vs fumble

botch up is not a noun while fumble is a noun.

Word	Noun	Adjective	Verb	Adverb
botch up	No	No	Yes	No
fumble	Yes	No	Yes	No

As verbs, botch up and fumble are synonyms defined as:

botch up (noun)	fumble (noun)
	(sports) dropping the ball

botch up (verb)	fumble (verb)
make a mess of, destroy or ruin	drop or juggle or fail to play cleanly a grounder
	feel about uncertainly or blindly
	handle clumsily
	make one's way clumsily or blindly
	make a mess of, destroy or ruin