high school vs senior high

high school and senior high both are nouns.

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

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

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

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

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