fit the bill vs fill

fit the bill is not a noun while fill is a noun.

Word	Noun	Adjective	Verb	Adverb
fit the bill	No	No	Yes	No
fill	Yes	No	Yes	No

As verbs, fill is a hypernym of fit the bill; that is, fill is a word with a broader meaning than fit the bill:

Other hypernyms of fit the bill include conform to, fit, fulfil, fulfill, meet, satisfy.

fit the bill (noun)	fill (noun)
	a quantity sufficient to satisfy
	any material that fills a space or container

fit the bill (verb)	fill (verb)
be what is needed or be good enough for what is required	become full
	make full, also in a metaphorical sense
	plug with a substance
	fill to satisfaction
	eat until one is sated
	fill, satisfy or meet a want or need or condition or restriction
	assume, as of positions or roles
	appoint someone to (a position or a job)
	occupy the whole of