literate vs writer

literate and writer both are nouns.

Word	Noun	Adjective	Verb	Adverb
literate	Yes	Yes	No	No
writer	Yes	No	No	No

As nouns, writer is a hyponym of literate; that is, writer is a word with a more specific, narrower meaning than literate:

Other hyponyms of literate include alphabetiser, alphabetizer, reader.

literate (noun)	writer (noun)
a person who can read and write	writes (books or stories or articles or the like) professionally (for pay)
	a person who is able to write and has written something

literate (adjective)	writer (adjective)
able to read and write
versed in literature; dealing with literature
knowledgeable and educated in one or several fields