old-timer vs greybeard

old-timer and greybeard both are nouns.

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

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

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

old-timer (noun)	greybeard (noun)
an elderly man	a stoneware drinking jug with a long neck; decorated with a caricature of Cardinal Bellarmine (17th century)
an experienced person who has been through many battles; someone who has given long service	a man who is very old