A short story is a short story. It can be about anything. A fairy tale is also a short story, but there is a magical or amazing element to it. If you think about the fairy tales you know, there is always some magic coming to the rescue or evil magic bothering the main character. If there is no magic, there is at least something impossible, like Goldilocks going to a house where bears live just like people. A fairy tale always has a nice, ordinary main character who overcomes some problem by unusual means. (Jack and the Beanstalk and Cinderella are good examples.) Some stories we call fairy tales are really just short stories or folk tales. They have a moral or lesson, but they are more amusing than magical. The Ugly Duckling is a good example.

i think a short story tends to be more realistic, while fairytale (as the name suggests) can be more imaginative, unreal. Fairytales tend to use simpler language, while short stories may be quite sophisticated in writing.

Both can teach a moral, but not necessarily so.

a short story can be like “see spot run…” while a fairytale usually begins with “once upon a time, there was a princess…”

both can teach a moral.

A short story can be about anything – true or made up and a fairytale is a made up story.