old man vs oldster

old man and oldster both are nouns.

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

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

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

old man (noun)	oldster (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