It's an age old question. Some pithy answers are:
"You don't spill beer on a violin!"
"When you are buying one, it’s a fiddle. When you are selling one, it’s a violin."
"A violin has strings, and a fiddle has STRANGS."
"A fiddle is a violin with attitude."
My absolute favorite, and I think the most accurate answer is:
"A violin sings, and a fiddle dances."
A fiddle is a dance instrument, it gets people moving. So when you play dance music on a violin - jigs, reels, hornpipes, polkas, and waltzes - you are fiddling. Which is why I call my violin a fiddle.
As far as the instrument itself goes, a violin is fiddle, but a fiddle is not necessarily a violin. A fiddle is a stringed instrument played with a bow. So a violin is a fiddle, which is the instrument I use - but so is a viola, and a cello, and a whole menagerie of related instruments: the hardanger fiddle, the rebec, the kit or pochette. The old adage that "Nero fiddled while Rome burned" may not be true, but if it is, he certainly did not play the violin, as the instrument wouldn't be invented for another fifteen hundred years. Sadly, the word "fiddle" has a bunch a negative connotations: "don't fiddle with that!" or "I fiddled away the time." For me, however, one of the most satisfying ways to spend time, is by fiddling.