The key difference is that the problem being solved is a math problem. It can be written down on paper.
A ball falling on the ground can be converted into a math problem. To get the conversion exactly right you will need to write down the exact state of the ball. But you will invariably incur small inaccuracies while doing this. For example, maybe the mass you write down is off by 1 part in a trillion. The math problem is the ground truth, so any conversion inaccuracies are now errors in the ball. In practice these inaccuracies will prevent even the original ball from solving the written down problem much better than you could with a computer.
In the case of random circuit sampling, the written down problem is a tensor network [1] (that happens to also be a shallow quantum circuit). Fundamentally, a tensor network just specifies a bunch of matrix multiplications to do. It's not even that big of a problem: only a few kilobytes of information (whereas the exact state of a ball would be gargantuan). All you have to do is perform the specified multiplications, interpret the result as a probability distribution, and sample from it. The obstacle is that these multiplications create intermediate values that are really really large. The quantum computer bypasses this obstacle by executing the tensor network as a circuit.
A ball falling on the ground can be converted into a math problem. To get the conversion exactly right you will need to write down the exact state of the ball. But you will invariably incur small inaccuracies while doing this. For example, maybe the mass you write down is off by 1 part in a trillion. The math problem is the ground truth, so any conversion inaccuracies are now errors in the ball. In practice these inaccuracies will prevent even the original ball from solving the written down problem much better than you could with a computer.
In the case of random circuit sampling, the written down problem is a tensor network [1] (that happens to also be a shallow quantum circuit). Fundamentally, a tensor network just specifies a bunch of matrix multiplications to do. It's not even that big of a problem: only a few kilobytes of information (whereas the exact state of a ball would be gargantuan). All you have to do is perform the specified multiplications, interpret the result as a probability distribution, and sample from it. The obstacle is that these multiplications create intermediate values that are really really large. The quantum computer bypasses this obstacle by executing the tensor network as a circuit.
[1]: https://en.wikipedia.org/wiki/Tensor_network