pupil vs school-age child

pupil and school-age child both are nouns.

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

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

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

Other synonyms of pupil include schoolchild.

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