Definition of fable - A short allegorical narrative making a moral point, traditionally by means of animal characters who speak and act like human beings.
Examples: Aesop's Fables,
Definition of folktale - A traditional narrative, usually anonymous, handed down orally - e.g., fables,fairy tales, legends, etc.
A tall tale is a special kind of hero story because the heroes of tall tales are 'larger than life'. An exaggerated, unreliable story: “My uncle claims that he was raised in a drainage ditch, but it's just another of his tall tales.” Examples: Paul Bunyan, Pecos Bill.
Fairy tale: One definition is a children's story about magical and imaginary beings and lands.
How are Fairy Tales different from Folk Tales?
Fairy tales are a subgenre of folk tales and almost always involve some element of magic and good triumphing over evil. A good rule of thumb: if there's a fairy or other mystical/magical creature in the story, it's a fairy tale.
(Source: Oklahoma State University Library)