old man vs graybeard

old man and graybeard both are nouns.

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

As nouns, old man and graybeard are synonyms defined as:

Other synonyms of old man include greybeard, Methuselah.

old man (noun)	graybeard (noun)
an informal term for your father	a man who is very old
a man who is very old
a familiar term of address for a man
(slang) boss
aromatic herb of temperate Eurasia and North Africa having a bitter taste used in making the liqueur absinthe