You will likely get several variations on the differences but to me, the major difference is a casual kilt has less material (about 4 yards) which translates into fewer, wider pleats and is cut so that it rides lower on the waist like jeans would be worn today. So instead of a 24" kilt length you may have a 22".

Some latitude should be understood given that some consider a traditional kilt to be a 4 yard box pleat kilt while others may consider it 8 yards knife pleat