greybeard vs old codger

greybeard and old codger both are nouns.

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

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

greybeard: a man who is very old
old codger: used affectionately to refer to an eccentric but amusing old man

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

greybeard (noun)	old codger (noun)
a stoneware drinking jug with a long neck; decorated with a caricature of Cardinal Bellarmine (17th century)	used affectionately to refer to an eccentric but amusing old man
a man who is very old