age vs second childhood

age and second childhood both are nouns.

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

As nouns, second childhood is a hyponym of age; that is, second childhood is a word with a more specific, narrower meaning than age:

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

Other hyponyms of age include dotage, senility, autumn years, decrepitude.

age (noun)	second childhood (noun)
how long something has existed	mental infirmity as a consequence of old age; sometimes shown by foolish infatuations
a time of life (usually defined in years) at which some particular qualification or power arises
a late time of life
an era of history having some distinctive feature
a prolonged period of time