Answer:
Step-by-step explanation:
Both are intended to teach. A parable in general teaches moral lessons and correct moral behavior. Parables in general have humans as central characters.
Jesus spoke in Parables. He told stories that showed (always) that there was a higher level of behavior that was more important than the lower level most obvious answer. You can read any one of them and pick that out as a conclusion. For example, the good Samaritan is about a man accosted on the road. The people that should have stopped to help him (priests and Levites returning from their duties) did not. But a man who was an enemy of the injured man not only stopped, he took the victim to a local inn to be tended for his woulds. Who showed the higher moral behavior?
On the other hand a fable is usually a tale involving a tale that has creatures in nature, who through their own folly do something that we should learn from.
One of Aesop's fables has to do with a Crane and a Wolf. A wolf get's a wishbone caught in his throat. He goes to a crane, offers a reward and tells her to pull it out which she does. The wolf begins to walk away, when the crane asks for her reward. The wolf says "Isn't it reward enough that I did not snap off your head when you had it down my throat?"
The moral is: don't expect rewards from those that are wicked. (That's what it says).