old person vs old man

old person and old man both are nouns.

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

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

old person (noun)	old man (noun)
an elderly person	an informal term for your father
	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