schoolchild vs school-age child

schoolchild and school-age child both are nouns.

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

As nouns, schoolchild and school-age child are synonyms defined as:

schoolchild and school-age child: a young person attending school (up through senior high school)

Other synonyms of schoolchild include pupil.

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