There are several types of essays, and only a narrative essay resembles a story. The traditional length of a narrative essay would be comparable only to a short story in length.
A narrative essay is, in essence, a short version of a personal story from a writer's experience. In some ways, a narrative essay and a short story can feel similar to one another. Both require a certain amount of imaginative narrative from the writer and use descriptive words to convey emotions, lay out the scene, and place the reader inside the events.
However, there are quite a few differences, which is why you won't find a narrative essay in a compilation book of short stories.
Like all other forms of essays, a narrative essay needs a clear outline of ideas that organize the writer's thoughts. Essays will always include an introduction, a body of writing, and a conclusion that sums up the writer's points or describe what the writer learned from the experience they write about.
Short stories need no such structure. While there is technically a beginning, a middle, and an end, the linear structure of a narrative essay is often not followed in a short story. Some jump around in time and play with the reader's imagination to determine the sequence of events and how one event affects or leads to another.
One of the most notable differences between a narrative essay and a short story is that a short story does not always have to be true. A story can be fiction or non-fiction, as both fit the definition of a short story. A narrative essay, on the other hand, is expected by the reader to be an actual experience from the writer's life.
The intent of an essay is always to inform, so readers have an expectation that they will learn something by reading an essay regardless of its form. When reading a narrative essay, a reader expects to learn more on the topic being discussed through first-hand knowledge due to the lived experience of the writer.
The intent of a story is to entertain. Some short stories are fables, which include a moral that teaches a lesson. However, even the best lessons in short stories will not come across or even be remembered if the story itself isn't engaging and entertaining.