letter paper vs writing paper

letter paper and writing paper both are nouns.

Word	Noun	Adjective	Verb	Adverb
letter paper	Yes	No	No	No
writing paper	Yes	No	No	No

As nouns, writing paper is a hypernym of letter paper; that is, writing paper is a word with a broader meaning than letter paper:

letter paper: paper cut to an appropriate size for writing letters; usually with matching envelopes
writing paper: paper material made into thin sheets that are sized to take ink; used for writing correspondence and manuscripts

As nouns, writing paper is a hypernym of letter paper; that is, writing paper is a word with a broader meaning than letter paper:

letter paper: writing paper for use in writing correspondence
writing paper: paper material made into thin sheets that are sized to take ink; used for writing correspondence and manuscripts

letter paper (noun)	writing paper (noun)
paper cut to an appropriate size for writing letters; usually with matching envelopes	paper material made into thin sheets that are sized to take ink; used for writing correspondence and manuscripts
writing paper for use in writing correspondence