informal vs cozy

informal is not a noun while cozy is a noun.

Word	Noun	Adjective	Verb	Adverb
informal	No	Yes	No	No
cozy	Yes	Yes	No	No

As adjectives, informal and cozy are synonyms defined as:

informal and cozy: having or fostering a warm or friendly and informal atmosphere

Other synonyms of informal include cosy, intimate.

informal (noun)	cozy (noun)
	a padded cloth covering to keep a teapot warm

informal (adjective)	cozy (adjective)
not formal	suggesting connivance
used of spoken and written language	enjoying or affording comforting warmth and shelter especially in a small space
having or fostering a warm or friendly and informal atmosphere	having or fostering a warm or friendly and informal atmosphere
not officially recognized or controlled