The short answer is nothing. The fiddle and violin are structurally the same instrument. It is the manner in which they are played that differ in addition to some set up and postural differences.
Structurally, the violin and the fiddle are the same – they are both wooden, curly body shaped with “s” shaped holes and 4 strings (some play with 5, but this is uncommon). Features like the types of strings used, the style and placement of the bridge and the way the instrument is tuned stylistically may be different, but a violinist could borrow their fiddler friend’s fiddle and play a classical piece and vice versa.
Historically, violin strings were made with catgut – which is actually sheep gut unlike the name implies, that has been dried and twisted into strings. Some players prefer to use catgut strings because they produce a distinct sound from aluminum or steel, but most players opt for the easier and more readily available metal strings.
Why is a string that is not and never was made from the guts of cats called “catgut”? Some people believe that catgut might be short for cattlegut as cows were one of the animals who gave up their intestines in the name of music. Still, others hypothesize that catgut was transformed from “kitgut” with “kit” being a slang for a fiddle when people mistakenly thought that kit was short for kitten. Kittengut? I imagine a demon in hell playing a violin made of bones and strung with kitten intestines. Thankfully, catgut isn’t quite that macabre. It is made from fibres found in the intestinal wall of sheep, goats, cattle, hogs, horses, donkeys or mules.
So there you have it; the difference between a violin and a fiddle with a little creepy mixed in for your reading displeasure.