A fairytale is a story,usually for children, about elves, hobgoblins, dragons, fairies,or other magical creatures that usually has a happy ending.
A fable is a short tale to teach a moral lesson, often with animals or objects as characters.
A myth is a story based on tradition or legend, which has a deep symbolic meaning. A myth 'conveys a truth' to those who tell it and hear it, rather than necessarily recording a true event. Although some myths can be accounts of actual events, they have become transformed by symbolic meaning or shifted in time or place. Myths are often used to explain universal and local beginnings and involve supernatural beings. The great power of the meaning of these stories, to the culture in which they developed, is a major reason why they survive as long as they do - sometimes for thousands of years.