school-age child vs pupil

school-age child and pupil both are nouns.

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

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

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

Other synonyms of school-age child include schoolchild.

school-age child (noun)	pupil (noun)
a young person attending school (up through senior high school)	the contractile aperture in the center of the iris of the eye; resembles a large black dot
	a learner who is enrolled in an educational institution
	a young person attending school (up through senior high school)