high school vs middle school

high school and middle school both are nouns.

Word	Noun	Adjective	Verb	Adverb
high school	Yes	No	No	No
middle school	Yes	No	No	No

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

high school: a public secondary school usually including grades 9 through 12
middle school: a school for students intermediate between elementary school and college; usually grades 9 to 12

Other hypernyms of high school include Gymnasium, lycee, lyceum, secondary school.

high school (noun)	middle school (noun)
a public secondary school usually including grades 9 through 12	a school for students intermediate between elementary school and college; usually grades 9 to 12