boarder vs school-age child

boarder and school-age child both are nouns.

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

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

boarder: a pupil who lives at school during term time
school-age child: a young person attending school (up through senior high school)

Other hypernyms of boarder include pupil, schoolchild.

boarder (noun)	school-age child (noun)
a tenant in someone's house	a young person attending school (up through senior high school)
a pupil who lives at school during term time
someone who forces their way aboard ship