day school vs school

day school and school both are nouns.

Word	Noun	Adjective	Verb	Adverb
day school	Yes	No	No	No
school	Yes	No	Yes	No

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

Other hypernyms of day school include schoolhouse.

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

day school (noun)	school (noun)
a school building without boarding facilities	a building where young people receive education
a private school taking day students only	the process of being formally educated at a school
a school giving instruction during the daytime	an educational institution
	a large group of fish
	a body of creative artists or writers or thinkers linked by a similar style or by similar teachers
	an educational institution's faculty and students
	the period of instruction in a school; the time period when school is in session

day school (verb)	school (verb)
	swim in or form a large group of fish
	educate in or as if in a school
	teach or refine to be discriminative in taste or judgment