I tried looking the question up on Google and different AI sources, but the answers I got were unclear. Someone I was talking with on Reddit suggested to me that a fable is a story that has fantastical elements, and features talking animals; and a parable is a story about the earthly and mundane that has a spiritual meaning. However, I noticed some flaws with these definitions. "The boy who cried wolf" is often considered a fable, yet it contains no fantastical elements, and involves no talking animals. On the other hand, the story of Adam and Eve is typically interpreted as a historical event, yet it does contain fantastical elements and talking animals.
Stories from Jesus such as "The prodigal son", "The good Samaritan", and "The parable of the ten virgins" are categorized as parables, and they are all earthly, grounded stories. However, the story of "Lazarus and the rich man" has some fantastical or supernatural elements, but is often still categorized as a parable.
At the same time, one might consider a story in Hinduism called "The story of Narada and Vishnu". This is a story where the devoted sage Narada asks the god Vishnu to teach him about maya, the concept of illusion. Vishnu agrees to teach Narada, but he first tells Narada he is thirsty, and asks Narada to fetch him some water. Narada complies. But before he is able to complete his task he becomes sidetracked, and ends up living an entire lifetime doing various things which have nothing to do with his initial task. After having lived an entire lifetime of events, Narada encounters a disaster which is about to claim his life. In his distress, he cries out to the gods for help. At that moment, Narada finds himself back at the very location of his initial task, with Vishnu telling him that only a few minutes have passed, and then asking, "Where is my water?" In that moment, Narada acknowledges that he has finally come to understand maya.
This story contains some fantastical elements, and it teaches a religious lesson, similar to the parables of Jesus. I would personally categorize this story as a parable. But can a Hindu story be a "parable", or is the word "parable" only reserved for the stories of Jesus? Is a "parable" a religious term in general, or only Christian?
Are there any categorical definitions for the terms "parable" and "fable", or do the terms merely have heuristical definitions? In other words, do "parable" and "fable" have strict, mutually exclusive definitions? Or do the words lack any clear-cut distinction between them, and hence can only be categorized roughly based on broad rules-of-thumb?