writer vs literate

writer and literate both are nouns.

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

As nouns, literate is a hypernym of writer; that is, literate is a word with a broader meaning than writer:

Other hypernyms of writer include literate person.

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

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