sign up vs sign on

sign up and sign on both are verbs.

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

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

Other synonyms of sign up include contract, sign.

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