old man vs greybeard

old man and greybeard both are nouns.

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

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

Other synonyms of old man include graybeard, Methuselah.

old man (noun)	greybeard (noun)
an informal term for your father	a stoneware drinking jug with a long neck; decorated with a caricature of Cardinal Bellarmine (17th century)
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