engage vs sign on

engage and sign on both are verbs.

Word	Noun	Adjective	Verb	Adverb
engage	No	No	Yes	No
sign on	No	No	Yes	No

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

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

engage (verb)	sign on (verb)
get caught	engage by written agreement
consume all of one's attention or time
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)