old codger vs greybeard

old codger and greybeard both are nouns.

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

As nouns, greybeard is a hypernym of old codger; that is, greybeard is a word with a broader meaning than old codger:

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

Other hypernyms of old codger include graybeard, Methuselah, old man.

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