Rolling speed = how fast the wheels turn, described in terms of forward speed. So it's the circumference of the wheels multiplied by their angular speed. And the wheels are not uncoupled from the plane they are driven by the plane. It was only assumed that the friction in the wheel bearings is irrelevant.

Forward movement of the plane = speed of the plane relative to something not on the treadmill. I guess I should have called it airspeed, which it would be if there is no wind.

Speed of the treadmill = how fast the surface of the treadmill moves.

And that is more time than I wanted to spend rehashing this old nonsense. The grandparent was only meant to explain why the great grandparent would not have settled the issue, not to settle it on its own. The only further comment I have is the whole thing is based on an unrealistic setup, which becomes incoherent if you assume that it is about real planes and real treadmills.