One way they are similar is that they both had the story about Jim Smiley and his jumping frog. Although, the story form went into greater detail with Andrew Jackson and the racing horse, they both had the main idea. One way they differ from each other is that the play form did not start with the narrator wanting to gain knowledge of Leo Smiley. The story form did start with it.
The theme of the story and the play were basically identical. To me, they both had the idea to teach kids or people to be wise with what you do with your money and don’t gamble.
Some characters that both the story and play had were Jim Smiley and the stranger.