essayist vs writer

essayist and writer both are nouns.

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

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

essayist: a writer of literary works
writer: writes (books or stories or articles or the like) professionally (for pay)

Other hypernyms of essayist include author.

essayist (noun)	writer (noun)
a writer of literary works	writes (books or stories or articles or the like) professionally (for pay)
	a person who is able to write and has written something