schoolboy vs school-age child

schoolboy and school-age child both are nouns.

Word	Noun	Adjective	Verb	Adverb
schoolboy	Yes	No	No	No
school-age child	Yes	No	No	No

As nouns, school-age child is a hypernym of schoolboy; that is, school-age child is a word with a broader meaning than schoolboy:

schoolboy: a boy attending school
school-age child: a young person attending school (up through senior high school)

Other hypernyms of schoolboy include boy, male child, adult male, man, pupil, schoolchild.

schoolboy (noun)	school-age child (noun)
a boy attending school	a young person attending school (up through senior high school)