The Merriam-Webster Dictionary defines a fable as a fictitious narrative or statement with the following aspects:
1. a legendary story of supernatural happenings
2. a narration intended to enforce a useful truth ; especially : one in which animals speak and act like human beings
3. falsehood, lie
The Visual Thesaurus provides a nice visualization of these three aspects or elements of fable. Each is represented by its own “branch.” I like to think of the image above as the fable’s “family tree.”
The first branch (the one sticking out to the right) is related to the first concept in Webster’s definition: a legendary story of supernatural happenings. The “fruit” on this branch is the word “legend.” Legends chronicle the lives of heros, saints, or other mythical figures. They are epic stories that can’t be verified by historical records.
The top branch represents the moral, spiritual, or instructional aspect of the fable. It corresponds to the second characteristic of fabels as defined in Webster: a narration intended to enforce a useful truth especially one in which animals speak and act like human beings. There are three words on this branch: allegory, apologue, and parable. Each word provides an additional nuance to our understanding of the fable’s intended value.
An allegory is a representation of abstract ideas or principles by characters, figures, or events in narrative, dramatic, or pictorial form. An allegory can be thought of as a prolonged metaphor.
Apologue
A story or relation of fictitious events, intended to convey some moral truth; a moral fable.
Note: An apologue differs from a parable in this: the parable is drawn from events which take place among mankind, and therefore requires probability in the narrative; the apologue is founded on supposed actions of brutes or inanimate things, and therefore is not limited by strict rules of probability. [AE]sop’s fables are good examples of apologues.
Webster’s Revised Unabridged Dictionary
Parable
A comparison; a similitude; specifically, a short fictitious narrative of something which might really occur in life or nature, by means of which a moral is drawn; as, the parables of Christ.
Webster’s Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
The bottom branch of this family tree emphasizes that fables are created in the human imagination. They are fictions or fabrications. Artful and deliberate literary inventions not necessarily based on fact.
The American Heritage® Dictionary of the English Language, Fourth Edition