high school vs senior high school

high school and senior high school both are nouns.

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

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

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

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

high school (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