engage vs employ

engage is not a noun while employ is a noun.

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

As verbs, employ is a hypernym of engage; that is, employ is a word with a broader meaning than engage:

Other hypernyms of engage include engage, hire.

As verbs, engage and employ are synonyms defined as:

Other synonyms of engage include hire.

engage (noun)	employ (noun)
	the state of being employed or having a job

engage (verb)	employ (verb)
get caught	put into service; make work or employ for a particular purpose or for its inherent or natural purpose
consume all of one's attention or time	engage or hire for work
give to in marriage
keep engaged
engage for service under a term of contract
hire for work or assistance
ask to represent; of legal counsel
engage or hire for work
carry out or participate in an activity; be involved in
carry on (wars, battles, or campaigns)