This all turns on what you mean by "completely different". Yes, obviously when you learn to actually catch a ball your brain is not doing anything that maps straightforwardly onto the kinds of symbolic manipulations that happen when you do math. On the other hand, it has to map onto doing math somehow even if that mapping is not straightforward. The only other possibility is that your brain is actually doing something that doesn't map onto math in any way, but still somehow produces the same results that math does by sheer coincidence. If you could actually demonstrate that, it would be one of the biggest breakthroughs in the history of science because it would refute the Church-Turing thesis.