highschool vs senior high school

highschool and senior high school both are nouns.

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

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

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

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

highschool (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