skyrocket vs move up

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

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

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

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

skyrocket (noun)	move up (noun)
sends a firework display high into the sky
propels bright light high in the sky, or used to propel a lifesaving line or harpoon

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