To say that a short story is a story which is short is begging the question. Such a definition does not explain what a story is or what is meant by "short." Edgar Allan Poe offered a thorough definition of the short story, and it has pretty much been the accepted definition since his day. Here is Poe's precise definition of the short story.
A skilful literary artist has constructed a tale. If wise, he had not fashioned his thoughts to accommodate his incidents; but having conceived, with deliberate care, a certain unique or single effect to be wrought out, he then invents such incidents--he then combines such events as may best aid him in establishing this preconceived effect. If his very initial sentence tend not to the outbringing of this effect, then he has failed in his first step. In the whole composition there should be no word written, of which the tendency, direct or indirect, is not to the one pre-established design. And by such means, with such care and skill, a picture is at length painted which leaves in the mind of him who contemplates it with a kindred art, a sense of the fullest satisfaction. The idea of the tale has been presented unblemished, because undisturbed; and this is an end unattainable by the novel. Undue brevity is just as exceptionable here as in the poem; but undue length is yet more to be avoided.
Edgar Allan Poe
A review of Hawthorne’s Twice-Told Tales
Graham’s Magazine, May, 1842
The two most important words in the above quotation are "single effect." A modern short story is intended to produce a single (emotional) effect. This can come at the end of the story or it can be evoked by the overall tone and mood. Poe does not specify what constitutes a "short" story, but the best definition is that it is a story that can be read in a single sitting. (Poe uses "single sitting" when writing about poetry.) If a story (or a poem) can't be read in a single sitting, it is unlikely to produce a single effect. So what is the definition of the word "story"? A story is a dramatic narrative. A short story is a dramatic narrative that is intended to be read at a single sitting. If it isn't dramatic it is nothing. Sometimes we expect to read a story at a single sitting and the phone rings or the nurse tells us the doctor is ready to see us or we forgot something we left cooking on the stove--but the author intended his story to be read at a single sitting from beginning to end. That is the main difference between a short story and a novel. The novelist does not intend to have his book read at a single sitting. That is why he divides it into chapters. These tell us where we can take a break. Now what is a "sitting"? Some people can sit longer than others. Some people read faster than others--much faster in some cases. (A speed reader could probably read one of Shakespeare's sonnets in three seconds--but I doubt he would get much out of it.) I can only suggest that a sitting should not last much longer than a college lecture, which is typically fifty minutes long because the professor knows that students get restless and start to fidget and tune him out. I further suggest that the length of a short story should be limited by the number of words that can be read aloud with appropriate feeling and emphasis in fifty minutes or one hour. That would equalize speed readers and slow readers. If you can read one hundred words a minute aloud, then a good approximate maximum length for a short story would be around six thousand words. A story like Shirley Jackson's "The Lottery" seems like the ideal length to me--and it certainly produces a single effect!
A short story is a dramatic narrative intended to be read at a single sitting and designed to produce a single effect.