fables — a short tale to teach a moral lesson, often with animals or inanimate objects as characters; apologue: the fable of the tortoise and the hare; Aesop's fables.
parables — a short allegorical story designed to illustrate or teach some truth, religious principle, or moral lesson.
stories — a narrative, either true or fictitious, in prose or verse, designed to interest, amuse, or instruct the hearer or reader; tale.