No. If the sun were always directly overhead this would be correct, but it isn't, so it isn't. The difference depends on the angle of the sun. In the middle of the day it's negligible, but at sunset and sunrise it becomes very large.
Mh no, the shadow's position depends not just on the planes movement, but also on earth's rotation and trajectory.
Is that not also true of the plane's projection onto the Earth's surface?
I think "trajectory" refers to the position of earth relative to sun, which affects the shadow but of course has no effect on the projection.
I don't think so, since projection would be like taking the line between the center of the earth and the plane and finding where that intersects the surface of the earth. That doesn't depend on the trajectory of the earth through space.
Whoops, I totally ignored the trajectory aspect and was just thinking both would be affected by the rate of rotation of the earth