full-grown vs adult

full-grown is not a noun while adult is a noun.

Word	Noun	Adjective	Verb	Adverb
full-grown	No	Yes	No	No
adult	Yes	Yes	No	No

As adjectives, full-grown and adult are synonyms defined as:

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

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

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