senior high school vs senior high

senior high school and senior high both are nouns.

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

As nouns, senior high school and senior high are synonyms defined as:

senior high school and senior high: a public secondary school usually including grades 9 through 12

Other synonyms of senior high school include high, high school, highschool.

senior high school (noun)	senior high (noun)
a public secondary school usually including grades 9 through 12	a public secondary school usually including grades 9 through 12