mature vs grow up

mature is an adjective but grow up is not an adjective.

Word	Noun	Adjective	Verb	Adverb
mature	No	Yes	Yes	No
grow up	No	No	Yes	No

As verbs, grow up is a hyponym of mature; that is, grow up is a word with a more specific, narrower meaning than mature:

Other hyponyms of mature include ripen, find, find oneself.

mature (adjective)	grow up (adjective)
having reached full natural growth or development
characteristic of maturity
(of birds) having developed feathers or plumage; often used in combination
fully developed or matured and ready to be eaten or used
fully considered and perfected

mature (verb)	grow up (verb)
cause to ripen and discharge pus	become an adult
develop and reach maturity; undergo maturation
grow old or older
become due for repayment
cause to ripen or develop fully
develop and work out fully in one's mind