William Boyd's Taxonomy of the Short Story

From this 2004 Guardian piece. Pared-down and lightly rearranged…

1 The event-plot story … The stereotype of the event-plot story is the “twist-in-the-tail” famously developed by O Henry but also used widely in genre stories – ghost stories (WW Jacobs, for example) and the detective story (Conan Doyle). I would say that today its contrivances make it look very dated, though Roald Dahl made something of a mark with a macabre variation on the theme, and it is also a staple of yarn-spinners such as Jeffrey Archer.

2 The Chekhovian story …  The revolution that Chekhov set in train – and which reverberates still today – was not to abandon plot, but to make the plot of his stories like the plot of our lives: random, mysterious, run-of-the-mill, abrupt, chaotic, fiercely cruel, meaningless. … I would say that the Chekhovian point of view is to look at life in all its banality and all its tragic comedy and refuse to make a judgment. To refuse to condemn and refuse to celebrate. To record the actions of human beings as they are and to leave them to speak for themselves (insofar as they can) without manipulation, censure or praise. …

3 The ‘Modernist’ story … Hemingway’s most obvious revolutionary contribution to the short story was his style: pared down, laconic, unafraid to repeat the most common adjectives rather than reach for a synonym. But his other great donation was a purposeful opacity. … You know there are hidden meanings here and it is the inaccessibility of the subtext that makes the story so memorable. Wilful obscurity in the short story works: over the length of a novel it can be very tiresome. This idea of modernist obscurity overlaps with the next category.

4 The cryptic/ludic story Here the story presents its baffling surface more overtly as a kind of challenge to the reader … In these stories there is a meaning to be discovered and deciphered … A Nabokov story, such as “Spring at Fialta”, is meant to be unravelled by the attentive reader – and it may take several goes – but the spirit behind its teasing is fundamentally generous: dig deep and you will discover more, is the implied message. …

5 The mini-novel story In a way it is something of a hybrid – half novel, half short story – trying to achieve in a few dozen pages what the novel achieves in a few hundred: a large cast of characters, lots of realistic detail. … These stories tend to be very long, almost becoming novellas, but their ambition is clear. They eschew ellipsis and allusion for an aggregation of solid fact, as if the story wants to say, “See: you don’t need 400 pages to paint a portrait of society.”

6 The poetic/mythic story … the poetic/mythic story seems to wish to get as far away from the realistic novel as possible. … This is the short story-quasi-poem and it can range from stream-of-consciousness to the impenetrably gnomic.

7 The biographical story … the short story deliberately borrowing and replicating the properties of non-fiction: of history, of reportage, of the memoir. … [A] variation is to introduce the fictive into the lives of real people. …  A very valid definition of biography is that it is “a fiction conceived within the bounds of the observable facts”. The biographical story plays with this paradox and in so doing attempts to have its cake and eat it, to capture the strengths of fiction and the non-fictional account simultaneously.

Seems good enough, for a start. Pair with this 2006 Boyd piece on the history of the short story. The commenter is right about Washington Irving.