father vs old man

father and old man both are nouns.

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

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

Other hyponyms of father include dad, dada, daddy, pa, papa, pappa, pop, father-in-law, pater.

father (noun)	old man (noun)
a male parent (also used as a term of address to your father)	an informal term for your father
the founder of a family	a man who is very old
a person who holds an important or distinguished position in some organization	a familiar term of address for a man
a person who founds or establishes some institution	(slang) boss
the head of an organized crime family	aromatic herb of temperate Eurasia and North Africa having a bitter taste used in making the liqueur absinthe

father (verb)	old man (verb)
make (offspring) by reproduction