Proverbs
The complete subject is "many fables." Fables are fictional stories that often involve animals or inanimate objects that teach a moral lesson or a practical truth.
The reader can find a universal truth from the details in the story
In a way you have to decide it yourself. Ask yourself what is the book trying to tell me? In a way it's like a moral of the story
The details from the story that suggest a universal truth
The details from the story that suggest a universal truth
Aesop is credited with fables, which are short stories that typically feature animals as characters and convey moral lessons. These fables often involve a moral or lesson at the end that teaches the reader a valuable principle or truth.
The term you are looking for is a fable. Fables are short stories, usually involving animals as characters, that convey a moral or lesson at the end. These stories often have improbable or fanciful elements but are meant to teach a valuable truth to the reader.
Always. The question that follows, however, is what are universal truths and where should they be taught. If the universal truth is the periodic nature of electron structure in chemical elements, which is a universal truth (and the underlying mechanism by which chemistry works), present it in science class in public school or anywhere it is appropriate. If the universal truth is that there is a God and He is the Creator of all things, then teach that in Church and at home as well as in private school, if desired.
The details from the story that suggest a universal truth
No, it is not a universal truth.
A Fable is just another word for 'story'. Usually when we talk about 'Fables' we mean 'a story with some kind of a moral lesson'. Aesop's Fables are typical Fables; and a story such as The Dog and the Bone has an obvious lesson to teach. Quite often Fables will have some element of magic or fantasy; and almost as often a Fable will have animals who can talk and think like humans as main characters. But these things are not necessary. Many fables are fantastical, or have animals as characters; but a fable such as Neruda's Mermaid and the Drunks delivers its moral lesson in an almost realistic narrative. A Fable can be a poem (Dryden and La Fontaine both wrote famous fables which are also poems); but it does not need to be (Aesop's Fables are often found as prose stories; and so are the fables in the Arabian Nights).
Fables and legends are from a different source. Fables are made up to express a point or moral. Legends have origins that may or may not have been true but are usually embellishments of the truth to emphasize the meaning of the story. So the answer to fables is no. Legends? Maybe.