engage vs fill

engage is not a noun while fill is a noun.

Word	Noun	Adjective	Verb	Adverb
engage	No	No	Yes	No
fill	Yes	No	Yes	No

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

Other hyponyms of engage include featherbed, engage, ship, contract, sign, sign on, sign up, rat, farm out, job, subcontract.

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

engage (verb)	fill (verb)
get caught	become full
consume all of one's attention or time	make full, also in a metaphorical sense
give to in marriage	plug with a substance
keep engaged	fill to satisfaction
engage for service under a term of contract	eat until one is sated
hire for work or assistance	fill, satisfy or meet a want or need or condition or restriction
ask to represent; of legal counsel	assume, as of positions or roles
engage or hire for work	appoint someone to (a position or a job)
carry out or participate in an activity; be involved in	occupy the whole of
carry on (wars, battles, or campaigns)