[LAGmaniac]

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sure they are - the conveyor velocity simply accelerates instantaneously with the wheel's tangential velocity.

but as Patrick said, these accelerations have absolutely nothing to do with the forward acceleration of the plane.

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But if there is any tangential velocity of the wheel with respect to the conveyor belt, doesn't that mean that they are operating at different speeds?

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Velocity at what point on the wheel? The only meaningful points in this context are the wheel center and where the wheel contacts the conveyor. The velocity at the wheel center is the same as the plane's velocity. The velocity where the wheel contacts the conveyor is the same as the conveyor and the velocity's magnitude varies linearly between these two points. In the general case, they're not the same.

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Well by this definition a stationary wheel is also moving at the same speed as the conveyor belt. (i.e. the velocity where the wheel contacts the conveyor is the same as the conveyor in that reference frame, 0.

If that's the case then the phrase "The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels", is more of a truism than a condition. This just states that the wheels won't slip on the runway.

It only makes sense as a condition if it refers to tangential velocity.