At first glance, the difference between a short story and novel seems to be one of length only. Certainly length is the most obvious, and defining, difference between the two, but I don’t think that’s the only difference, or even the most important difference.
The short story lives and dies on the ability of the writer to grab a reader’s attention very quickly and then introduce characters and a situation and then resolve the whole thing in a very brief amount of time. Many short stories are less than 50 pages, a far cry from the 300 pages that often seems nothing more than a starting point for most novels. Brevity is the key here, giving the reader a complete story in what amounts to a few chapters. Most novels would just be getting started at that length, to say nothing of sequels. A short story can always be fleshed out, but it seems far more difficult to take a long story and then cut it down.
The full novel, on the other hand, allows the writer free reign, comparatively, to expand and flesh out, offering a sweeping story filled with characters, places, and turns of plot that gobble up space at a very rapid rate. But it also comes with it the temptation to keep adding and adding, until the story is so bulky and unwieldy as to be nearly overwhelming. Any given book in the Wheel of Time series is 700-800+ pages and there’s-what?-13 books now? It’s certainly not something you pick up on a whim, though fans of the series aren’t likely to complain about such a thing.
What this comes back to is the importance difference: purpose. A short story must have a clear purpose, a clear point it’s trying to get across, and it must get that point across in a very limited space. It requires the writer to carve away the elements that, while interesting in their own right, may not be entirely essential, much more so than a full length novel. In this way, the short story offers a clear, concise window into a world and its characters, because it has to. Sub-plots? Large cast? Broad setting? Those are for the novel.