senior high vs senior high school

senior high and senior high school both are nouns.

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

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

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

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

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