greybeard vs old geezer

greybeard and old geezer both are nouns.

Word	Noun	Adjective	Verb	Adverb
greybeard	Yes	No	No	No
old geezer	Yes	No	No	No

As nouns, old geezer is a hyponym of greybeard; that is, old geezer is a word with a more specific, narrower meaning than greybeard:

Other hyponyms of greybeard include codger, old codger, antique, gaffer, old-timer, oldtimer, patriarch.

greybeard (noun)	old geezer (noun)
a stoneware drinking jug with a long neck; decorated with a caricature of Cardinal Bellarmine (17th century)	an elderly man
a man who is very old