high school vs highschool

high school and highschool both are nouns.

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

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

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

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

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