sign up vs engage

sign up and engage both are verbs.

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

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

Other hypernyms of sign up include employ, hire.

sign up (verb)	engage (verb)
join a club, an activity, etc. with the intention to join or participate	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)