If we're getting clinical I believe fables have a more structured and poetical writing style but past that their is very little difference between them and fairy tales. If you want me to choose I'll say write a fairy tale but I don't believe there is much difference.

Also I believe the earliest written fables date back to Greece in 550 BC but as a style of story telling that was propagated by oral tradition it is more than likely that they are older than that.