It's pretty much clear how this goes. Flash fiction had always been my thing before i got to realize it had the name. It offers a quick read when one is on the go and keeps the reader's interest piqued.
Would fables be categorized as flash fiction too? I mean, they're fictional and a lot of them could be short and concise as well.
Some are, yes. So long as they are concise and straight to the point. Longer fables, however, can be categorised under short stories.