old man vs patriarch

old man and patriarch both are nouns.

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

As nouns, patriarch is a hyponym of old man; that is, patriarch is a word with a more specific, narrower meaning than old man:

Other hyponyms of old man include codger, old codger, antique, gaffer, old-timer, old geezer, oldtimer.

old man (noun)	patriarch (noun)
an informal term for your father	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
a familiar term of address for a man	title for the heads of the Eastern Orthodox Churches (in Istanbul and Alexandria and Moscow and Jerusalem)
(slang) boss	a man who is older and higher in rank than yourself
aromatic herb of temperate Eurasia and North Africa having a bitter taste used in making the liqueur absinthe