senior high school vs high school

senior high school and high school both are nouns.

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

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

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

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

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