Thanks for a fantastic question! This is difficult to answer, but I will give it ago.
The short answer is that brains control everything we do and all the skills we learn, so if you are very good at something then your brain must be slightly different to someone who isn’t as good at the same thing. Whether we can actually measure that difference because it may be only a very minor change is another question.
The other issue is whether child prodigies are actually born with different brains that give them their skills or whether they develop their brains through experience. I would say that it is probably a bit of both. Even if the parts of the brain that control finger movements and musical ability work ‘better’ in a child prodigy they would still need to practice to learn to play the piano – most child prodigies start learning something very young but they still practice very hard.
There is a very cool example of learning changing people’s brains from a study that looked at London taxi drivers. A group of scientists at University College London found that because taxi drivers have to learn and remember so many routes their hippocampus (a part of the brain involved in memory) is much bigger than other people’s. It is unlikely that the taxi drivers were born ‘map learning prodigies’, instead their brains changed as they learned. Fantastic news for all of us if we work hard 🙂