fully grown vs adult

fully grown is not a noun while adult is a noun.

Word	Noun	Adjective	Verb	Adverb
fully grown	No	Yes	No	No
adult	Yes	Yes	No	No

As adjectives, fully grown and adult are synonyms defined as:

Other synonyms of fully grown include big, full-grown, grown, grownup.

fully grown (noun)	adult (noun)
	any mature animal
	a fully developed person from maturity onward

fully grown (adjective)	adult (adjective)
(of animals) fully developed	(of animals) fully developed
	designed to arouse lust