old boy vs oldster

old boy and oldster both are nouns.

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

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

Other hypernyms of old boy include golden ager, old person, senior citizen.

old boy (noun)	oldster (noun)
a vivacious elderly man	an elderly person
a former male pupil of a school
a familiar term of address for a man