old man vs old person

old man and old person both are nouns.

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

As nouns, old person is a hypernym of old man; that is, old person is a word with a broader meaning than old man:

Other hypernyms of old man include adult male, man, golden ager, oldster, senior citizen.

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