Flash
An editor can call flash fiction, or anything else, whatever he wants. But technically, from 1,000--2,000 words is a short short.
Flash fiction is really anything from 100--1,000 words, but when a specific editor tells you he wants flash fiction up to 500 words, or up to 1,000 words, or even up to 1,500 words, he isn't defining the category, he's simply telling you how much space he has in his particular magazine, and how short or long he enjoys reading such stories.
Trouble comes when someone reads these guidelines and uses them as a definition of the category itself.