well,the feathers typically are ground slightly differently. If you view them as you said, there is a portion of the feather shaft that sticks out on the side opposite of "the wing" it came from. In othe words, left wing feathers stick out on the right side, right wing feathers on the left.
Yes, the feathers curve differently than the other type. Imagine the wing, each is cupped slightly to catch the air. Cup your hands and you can visualize. Since the feather itself is not symetrical, leading edge is small, following edge is larger, only one side (larger)of the feather is used for fletching.
I have never fletched right feathers with a left jig and vice versa but I would think it wouldn't work well due to those differing cup shapes.
If you carefully look at your fletch, on the arrow, left wing makes the arrow spin counter clock-wise, right wing goes the other way.
ChuckC