school-age child vs schoolchild

school-age child and schoolchild both are nouns.

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

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

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

Other synonyms of school-age child include pupil.

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