age vs nonage

age and nonage both are nouns.

Word	Noun	Adjective	Verb	Adverb
age	Yes	No	Yes	No
nonage	Yes	No	No	No

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

age: a time of life (usually defined in years) at which some particular qualification or power arises
nonage: any age prior to the legal age

Other hyponyms of age include age of consent, legal age, majority, minority, drinking age, voting age.

age (noun)	nonage (noun)
how long something has existed	any age prior to the legal age
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