Both running and driving are moving over the ground but with entirely different mechanisms.
I imagine saying the LLM has thoughts is like pretending the car has wheels for legs and is running over the ground. It is not completely wrong but misleading and imprecise.
That is pretty much an accurate discription of what planes and birds do.
To plan means "to reason with intent".
That is very much not what LLMs do, and the paper does not provide evidence to the contrary. Yet it uses the term to give credence to it's rather speculative interpretation of observed correlation as causation.
Interestingly enough there is no definition of the term, which at least would help to understand what the authors actually mean.
I would be more inclined to take a more positive stance to the paper if it used more appropriate terms, such as call observed correlations just that. Granted that would possibly make for much less of a fancy title.