Fable, n.
Etymology: [F., fr. L. fabula, fr. fari to speak, say. See Ban, and cf. Fabulous, Fame.]
1. A Feigned story or tale, intended to instruct or amuse; a fictitious narration intended to enforce some useful truth or precept; an apologue. See the Note under Apologue. Jotham's fable of the trees is the oldest extant. Addison .
2. The plot, story, or connected series of events, forming the subject of an epic or dramatic poem. The moral is the first business of the poet; this being formed, he contrives such a design or fable as may be most suitable to the moral. Dryden.
3. Any story told to excite wonder; common talk; the theme of talk. "Old wives' fables. " 1 Tim. iv. 7. We grew The fable of the city where we dwelt. Tennyson.
4. Fiction; untruth; falsehood. It would look like a fable to report that this gentleman gives away a great fortune by secret methods. Addison.
2 other Webster entries under this spelling
Fable, v. i. [imp. & p. p. Fabled; p. pr. & vb. n. Fabling.]
To compose fables; hence, to write or speak fiction ; to write or utter what is not true. "He Fables not." Shak. Vain now the tales which fabling poets tell. Prior. He fables, yet speaks truth. M. Arnold.
Fable, v. t.
To fiegn; to invent; to devise, and speak of, as true or real; to tell of falsely. The hell thou fablest. Milton.
Shades of meaning
Fernald has no entry of its own for fable; he lists it under allegory, fiction.
Where he writes about it:
The allegory, parable, or fable tells its story as if true, leaving the reader or hearer to discover its fictitious character and learn its lesson. — from allegory
An allegory is a moral or religious tale, of which the moral lesson is the substance, and all descriptions and incidents but accessories, as in "The Pilgrim's Progress." A fable is generally briefer, representing animals as the speakers and actors, and commonly conveying some lesson of practical wisdom or shrewdness, as "The Fables of AEsop." A parable is exclusively moral or religious, briefer and less adorned than an allegory, with its lesson more immediately discernible, given, as it were, at a stroke. — from allegory
The moral of the fable is expressed formally; the lesson of the fiction, if any, is inwrought. — from fiction
Apologue, a word simply transferred from Greek into English, is the same as fable. — from fiction