sign on vs sign up

sign on and sign up both are verbs.

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

As verbs, sign on and sign up are synonyms defined as:

Other synonyms of sign on include contract, sign.

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