school paper vs school newspaper

school paper and school newspaper both are nouns.

Word	Noun	Adjective	Verb	Adverb
school paper	Yes	No	No	No
school newspaper	Yes	No	No	No

As nouns, school paper and school newspaper are synonyms defined as:

school paper and school newspaper: a newspaper written and published by students in a school

school paper (noun)	school newspaper (noun)
a newspaper written and published by students in a school	a newspaper written and published by students in a school