sign up vs enlist

sign up and enlist both are verbs.

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

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

sign up: join a club, an activity, etc. with the intention to join or participate
enlist: join the military

sign up (verb)	enlist (verb)
join a club, an activity, etc. with the intention to join or participate	join the military
engage by written agreement	engage somebody to enter the army
	hire for work or assistance