school newspaper vs school paper

school newspaper and school paper both are nouns.

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

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

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

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