old codger vs graybeard

old codger and graybeard both are nouns.

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

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

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

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

old codger (noun)	graybeard (noun)
used affectionately to refer to an eccentric but amusing old man	a man who is very old