folly vs fatuity

folly and fatuity both are nouns.

Word	Noun	Adjective	Verb	Adverb
folly	Yes	No	No	No
fatuity	Yes	No	No	No

As nouns, fatuity is a hyponym of folly; that is, fatuity is a word with a more specific, narrower meaning than folly:

Other hyponyms of folly include indiscretion, injudiciousness, absurdity, fatuousness, silliness, asininity.

folly (noun)	fatuity (noun)
foolish or senseless behavior	a ludicrous folly
a stupid mistake
the trait of acting stupidly or rashly
the quality of being rash and foolish