What are the differences in folk tale aesop fable and fairy tale?

Folk tales are traditional tales told in all pre-industrial societies. Folk tales may be stories of traditional heroes (Havelok, Roland, Robin Hood) or of semi-mythical creatures (elves, tokoloshe, djinn). The people who tell such stories do not particularly think of the stories as fictional: in many cases they actually believe the tales of Robin Hood, and that brownies sour milk left out at night, though sometimes they 'keep an open mind' on such matters.

Fables are one step away from such folk gullibility. Fables are often based on folk-tales, but people tell a fable because it has a moral. Someone who tells the story of the Fox and the Grapes does not believe that any fox can really talk - but they recognise that there is a lesson in the story which you can appreciate even though the events are not literally true. (Aesop was a famous author / collector of fables - but there have been many others, including Phaedrus, La Fontaine, and Terry Jones of Monty Python).

A fairy tale is a deliberately made-up story. The people who write fairy tales do not believe fairies really exist, nor do they have a moral to convey - they simply want to write a pretty story about fairies. Fairy tales are much more modern than either folk tales or fables - fairy tales really only begin around the Eighteenth Century (before that people weren't sufficiently sure that fairies were not real).