patriarch vs graybeard

patriarch and graybeard both are nouns.

Word	Noun	Adjective	Verb	Adverb
patriarch	Yes	No	No	No
graybeard	Yes	No	No	No

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

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

patriarch (noun)	graybeard (noun)
the male head of family or tribe	a man who is very old
any of the early biblical characters regarded as fathers of the human race
title for the heads of the Eastern Orthodox Churches (in Istanbul and Alexandria and Moscow and Jerusalem)
a man who is older and higher in rank than yourself