<Sigh> Intelligence is an inherited trait. And then it is how you apply that trait that influences your abilities. I’m not sure how much more I can explain this - if you are born with it, it is a genetic trait. If you are not born with it, it is an ability. You are born with blue eyes, you cannot acquire them by trying hard. But you are not born knowing how to play chess. You are born with a degree (or not) of intelligence, and if you LEARN it you can become a chess player of varying levels. Anyone can actually learn how to play chess, it is a learned ability. But people who were born with the right sort of intelligence, a genetic trait, can apply that to learning chess and could become better at it than less intelligent people, but there is a possibility that a less intelligent person who has been brought up with chess and who’s family plays it often will acquire the ability to play it very well. People who do unusually well in things are often people who have had the good fortune to be born with genetic traits and then combined them with hard work and applied learning.
The British Olympic Go for Gold program from a couple of decades ago, which saw the rise of the cycling, rowing and skeleton teams in Summer and Winter Olympics employed this to great success. They invited people to be tested for natural abilities - and these natural abilities were parameters such as thigh length (genetic,) height (genetic,) explosive speed (acquired, but with a genetic element,) and so on. They fed the results into a computer program which identified if this person would be a good rower, cyclist or skeleton racer, regardless of whether they had ever done that sport before.
I know an Olympic gold medallist’s mum, and she said her daughter had never even heard of skeleton when she applied to be tested. I also saw a rower win gold in Rio, she had been a teacher before selection and had never rowed. They
were not born with the ability to win these sports, they learned how to win at them, using genetic traits.
Going back to your chess champions/musical prodigies/maths Olympians, those people are not born that way. They have been born with genetic traits that will give them a natural advantage. But the maths and music are learned abilities.