second childhood vs old age

second childhood and old age both are nouns.

Word	Noun	Adjective	Verb	Adverb
second childhood	Yes	No	No	No
old age	Yes	No	No	No

As nouns, old age is a hypernym of second childhood; that is, old age is a word with a broader meaning than second childhood:

second childhood: mental infirmity as a consequence of old age; sometimes shown by foolish infatuations
old age: a late time of life

Other hypernyms of second childhood include age, eld, geezerhood, years.

second childhood (noun)	old age (noun)
mental infirmity as a consequence of old age; sometimes shown by foolish infatuations	a late time of life