rocket vs move up

rocket is a noun but move up is not a noun.

Word	Noun	Adjective	Verb	Adverb
rocket	Yes	No	Yes	No
move up	No	No	Yes	No

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

Other hypernyms of rocket include arise, come up, go up, lift, rise, uprise.

rocket (noun)	move up (noun)
a jet engine containing its own propellant and driven by reaction propulsion
any vehicle self-propelled by a rocket engine
sends a firework display high into the sky
propels bright light high in the sky, or used to propel a lifesaving line or harpoon
erect European annual often grown as a salad crop to be harvested when young and tender

rocket (verb)	move up (verb)
propel with a rocket	move upward
shoot up abruptly, like a rocket	move to a better position in life or to a better job