Allegory, Parable, Myth and Fable are comparable as literary forms that typically tell a story for the sake of presenting a truth or of enforcing a moral.
An allegory veils its true meaning (its underlying or allegorical sense) by leaving it to be deduced from the story it tells (the outward or literal sense). Its characters and incidents are therefore either figurative or typical; they serve as a bait to the consideration of dull or unpleasant truths (as in Bunyan’s Pilgrim’s Progress), as a graded approach to the apprehension of ideas too difficult for the ordinary man (as in Dante’s Divine Comedy), or as a cloak for an attack on persons (as in Dryden’s Absalom and Achitophel) or for an exposure of vices and follies (as in Swift’s Gulliver’s Travels).
When the allegory is very short and simple and narrates or describes a familiar occurrence in nature or life that by analogy conveys a spiritual truth, it is called a parable. The term is specifically applied to the brief allegories used by Jesus in his sermons (as the one likening the kingdom of heaven to the growth of a mustard seed).
Myth is applied to a type of brief allegory used especially by Plato in expounding a difficult philosophical conception. Such myths are, as a rule, invented and their characters and incidents are purely imaginary.
In a fable the moral is usually clearly stated at the end. Its characters are animals (as in Orwell’s Animal Farm) or inanimate things that by talking and acting as human beings reflect the weaknesses and follies of men.