highschool vs senior high

highschool and senior high both are nouns.

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

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

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

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

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