jump-start vs start up

jump-start is a noun but start up is not a noun.

Word	Noun	Adjective	Verb	Adverb
jump-start	Yes	No	Yes	No
start up	No	No	Yes	No

As verbs, start up is a hypernym of jump-start; that is, start up is a word with a broader meaning than jump-start:

jump-start: start (a car engine whose battery is dead) by connecting it to another car's battery
start up: get going or set in motion

Other hypernyms of jump-start include start.

jump-start (noun)	start up (noun)
starting an automobile engine that has a weak battery by means of jumper cables to another car

jump-start (verb)	start up (verb)
start or re-start vigorously	get off the ground
start (a car engine whose battery is dead) by connecting it to another car's battery	get going or set in motion