school system vs school

school system and school both are nouns.

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

school system (noun)	school (noun)
establishment including the plant and equipment for providing education from kindergarten through high school	a building where young people receive education
	the process of being formally educated at a school
	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

school system (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