Sandwich is/can be more elaborate. A butty is thrown together quickly; the best example is the chip (french fries) butty, two slices of bread, any bread, and a handful of chips. Or even (and that holds for the bacon butty too), a single soft slice of bread, something on it, then folded in half. Jam butty, chip butty, bacon butty.

Sandwich is posh. Butty is folkie food.