When I finish a quilt, I use a double-fold binding. Some folks call this a French Binding. But I'm not that fancy. It's double-fold to me. The two photos show different ways of attaching the binding to the quilt back. In the first photo, if you click on the photo a close up will clearly show that you can see the hand stitches.
In the second photo, the stitches cannot be seen. The second photo (green binding) is the way I hand stitch the binding to the quilt backs. I don't think it takes any more time to "hide" the stitches under the edge of the binding than to have them show.