Creative writing, generally speaking, refers to original literary material someone creates. This can be stories, novels, creative essays, poetry, or other literary forms. Critical writing, on the other hand, is written material, generally in the form of essays, that discusses the literary work of another author or authors. Critical writing seeks to make an argument or express an opinion and uses evidence from the texts in question to support those arguments. In this sense, critical writing is always based on the texts under analysis; although, the argument an author makes about the text(s) can be thought of as "creative."
Poe did both kinds of writing. His famous poem, "The Raven," is an example of creative writing, in that Poe invented the entirety of the poem. On the other hand, his essay "The Philosophy of Composition" is an example of critical writing. In that essay, Poe uses the text of "The Raven" to make an argument about his own poetic method.