There are a few:
Both butterflies and moths start off as caterpillars but butterflies make a chrysalis and moths make a cocoon.
The antennae on butterflies and moths are also different.
Moths, on the other had, have more comb-like or feathery antennae.
Another difference is in their bodies.
Where as moths have stout, furry bodies.
One other difference I would point out is their typical resting position.
Moths tend to rest with their wings out.