poet vs writer

poet and writer both are nouns.

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

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

poet: a writer of poems (the term is usually reserved for writers of good poetry)
writer: writes (books or stories or articles or the like) professionally (for pay)

Other hypernyms of poet include author.

poet (noun)	writer (noun)
a writer of poems (the term is usually reserved for writers of good poetry)	writes (books or stories or articles or the like) professionally (for pay)
	a person who is able to write and has written something