It's a simple task to define the short story in opposition to other literary genres, even in purely qualitative terms. The short story is distinct from a novel (or, for that matter, a short extract from a novel) in many ways: the protagonist of a short story doesn't have to be fully 'back-storied', they can remain fairly anonymous, we don't need a family tree for them; nor do they need to be the sort of ultimately-likeable everyman that so dominates the novel (we don't have to get on with the start of a short story, the way we have to get on with a novel's central character as a 'fellow traveller' in the long 'plotted' course that is the novel's journey).
Equally the moral compass of a short story doesn't have to be as fixed as the novel's, there doesn't have to be that cumulative truth you find in a novel, always building and pointing in the same direction; as Nadine Gordimer argues, the short story's truth is momentary, discrete and fleeting, and as such the story can occupy a more morally ambiguous (and therefore realistic) universe. Also, we might distinguish the short story's revelation - and the nature of it - as being of a more singular, untempered variety than a novel's (if the novel trades in revelation at all).
Conversely, and at another level, the novel could claim greater realism for reflecting the fact that any chain of consequences leading from a single act is indefinitely long, all relationships go on, arguably, forever. Whilst in a short story, they are re-defined suddenly at the close, and then abandoned in a kind of unchanging stasis.
However, in trying to understand how a short story works on its own terms, short shrift will come from mere comparisons with the novel. What we need to talk about are the autonomous structures that make up the wider species we call short fiction. For the purposes of this Resource, we suggest the form be regarded in terms of three structural types - as discussed in more detail in the introduction to Parenthesis (2006) - namely: Epical, Lyrical & Artifice.
Please note many of the arguments in the Parenthesis introduction draw from the essays gathered in Charles E May's books: Short Story Theories (1977) and New Short Story Theories (1994).