senior high vs middle school

senior high and middle school both are nouns.

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

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

senior high: 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 senior high include Gymnasium, lycee, lyceum, secondary school.

senior high (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