day boarder vs school-age child

day boarder and school-age child both are nouns.

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

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

day boarder: a schoolchild at a boarding school who has meals at school but sleeps at home
school-age child: a young person attending school (up through senior high school)

Other hypernyms of day boarder include pupil, schoolchild.

day boarder (noun)	school-age child (noun)
a schoolchild at a boarding school who has meals at school but sleeps at home	a young person attending school (up through senior high school)