I got my numbers from my college professors. Our differing numbers are a good demonstration that word length is often determined by genre and what sells, and that there isn't a standard. What it'll be called will depend on who publishes it, and you'll have to check and see the common word lengths for the genre you want to publish in and the markets you're looking at.
Actually, the numbers I gave are standard, have been for pretty much a hundred years. Almost everyone out there follows them, with the only exception being a few thousand words on the novella and novel.
They're standard for the same reason that proofreaders' marks are standard. You have to have some system that allows everyone, everywhere to stay on the same page, that allows everyone to ask for the same thing without having to go into too many details each time.
I usually round off, but maybe that's a bad idea.
Under 100 words -- Micro fiction.
Under 1,000 words -- Flash fiction.
1,000-1,999 words --short-short.
2,000-7,500 words --short story.
7,501-15,000 words --novelette. (7,501-17,500 in SF & Fantasy.)
15,001-29,999 worsa --Novella. (17,501-39,999 in SF & fantasy,)
30,000 to infinity -novel. (40,000 to infinity in SF & fantasy.)
Now, it's common for any magazine to use shorthand and write "We use stories up to 25,000 words" or something similar. But thiis just shorthand.
There's another, very important reason, for these length guidelines. Just as a novel is not simply a very long short story, and can't be written the same way, neither is a novella just a long short story, nor is a novelette just a very long short-short.
Each has its own requirements, and its own method of telling. No matter how well you write it, a 25,000 word short story is going to be boring as hell. A 25,000 word novella, however, may be the most exciting form of fiction there is.
College professors are not a good source for accurate information about writing or publishing.