junior high school vs junior high

junior high school and junior high both are nouns.

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

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

junior high school and junior high: a secondary school usually including 7th and 8th grades

junior high school (noun)	junior high (noun)
a secondary school usually including 7th and 8th grades	a secondary school usually including 7th and 8th grades