old-timer vs graybeard

old-timer and graybeard both are nouns.

Word	Noun	Adjective	Verb	Adverb
old-timer	Yes	No	No	No
graybeard	Yes	No	No	No

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

Other hypernyms of old-timer include greybeard, Methuselah, old man.

old-timer (noun)	graybeard (noun)
an elderly man	a man who is very old
an experienced person who has been through many battles; someone who has given long service