A Fable is a short, fictional tale which has a specific moral or behavioral lesson to teach (Grenby).
Fairy Tales are narratives out of the folk tradition, set in an indeterminate past and typically including some enchantment or sense of the wondrous (Cullinan).
Folklore is the beliefs, customs, legends, and traditions that are handed down, generation after generation, in cultures all over the world (Cullinan).
Fractured Fairy Tales are based on traditional tales but retold with a twist such as role reversals, alternate endings, and changes to characters or settings.
Myths & Legends arose and were passed down as people searched to explain the origins of earth, sky, humans, and human behaviors (Cullinan).
References
Cullinan, Bernice E. and Diane G. Person. The Continuum Encyclopedia of Children's Literature. Continuum International Publ, 2005.
Grenby, M. O. Children's Literature. Vol. 2nd edition, Edinburgh University Press, 2014. EBSCOhost.