highschool vs middle school

highschool and middle school both are nouns.

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

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

highschool: 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 highschool include Gymnasium, lycee, lyceum, secondary school.

highschool (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