Allegories, Fables, Myths, Parables, What's the Difference? Options

[Cleo_Serapis]

An allegory is a form of extended metaphor, in which objects, persons, and actions in a narrative, are equated with the meanings that lie outside the narrative itself. The underlying meaning has moral, social, religious, or political significance, and characters are often personifications of abstract ideas as charity, greed, or envy.Thus an allegory is a story with two meanings, a literal meaning and a symbolic meaning.  
Example:
Fairie Queen by Edmund Spenser; Pilgrim's Progress by John Bunyan; Young Goodman Brown by Nathaniel Hawthorne

A fable is a story with a moral or lesson to impart, often through the actions of animals that speak and act like people; one extended sense is pejorative: fables never really happen, so they’re lies.

An Æsop Fable...

The Lion and the Mouse
ONCE when a Lion was asleep a little Mouse began running up and down upon him; this soon wakened the Lion, who placed his huge paw upon him, and opened his big jaws to swallow him. “Pardon, O King,” cried the little Mouse: “forgive me this time, I shall never forget it: who knows but what I may be able to do you a turn some of these days?” The Lion was so tickled at the idea of the Mouse being able to help him, that he lifted up his paw and let him go. Some time after the Lion was caught in a trap, and the hunters, who desired to carry him alive to the King, tied him to a tree while they went in search of a waggon to carry him on. Just then the little Mouse happened to pass by, and seeing the sad plight in which the Lion was, sent up to him and soon gnawed away the ropes that bound the King of the Beasts. “Was I not right?” said the little Mouse.
       “LITTLE FRIENDS MAY PROVE GREAT FRIENDS.”

A parable is a brief story told to illustrate a moral or religious idea.

A myth is a narrative that explains the prehistory of a people, often dealing with their origins and their gods; by extension it is a modern effort to represent the origins and values of a race or nation, and, by the very nature of its imaginative qualities, it has acquired pejorative senses.