on paper vs in writing

on paper is not an adjective while in writing is an adjective.

Word	Noun	Adjective	Verb	Adverb
on paper	No	No	No	Yes
in writing	No	Yes	No	Yes

As adverbs, on paper and in writing are synonyms defined as:

on paper (adjective)	in writing (adjective)
	written or drawn or engraved

on paper (adverb)	in writing (adverb)
as written or printed	as written or printed
in theory; according to the assumed facts