mistake vs fall for

mistake is a noun but fall for is not a noun.

Word	Noun	Adjective	Verb	Adverb
mistake	Yes	No	Yes	No
fall for	No	No	Yes	No

As verbs, fall for is a hyponym of mistake; that is, fall for is a word with a more specific, narrower meaning than mistake:

Other hyponyms of mistake include misremember, slip up, stumble, trip up, misjudge.

mistake (noun)	fall for (noun)
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

mistake (verb)	fall for (verb)
to make a mistake or be incorrect	fall in love with; become infatuated with
identify incorrectly	be deceived, duped, or entrapped by