I can speak from the chess world, as a coach. I used to believe there was really no such thing as talent largely based on my own experience as I started relatively late, don't consider myself talented, and reached a reasonably high level at the game. I kind of still do think there's no such thing as talent, but that comes with a bunch of asterisks.
If you take two people and expose them to normal training regimens, different people will have different results - and frequently extremely different results. One could argue that the person who performed worse might have performed better if given exposure to a different regimen but in practice I find those that tend to overperform in one regimen tend to overperform in other regimens as well.
The catch is that the outcome is largely predicted by how the student responds to the training itself. The person who finds it interesting and enjoyable is going to dramatically outperform compared to the person who may be highly motivated by an outcome (wanting to become a good player) but doesn't especially enjoy the process - tactical training, game analysis, etc.
And so talent may not just be some innate ability at something but rather an innate preference, which is going to be the product of a million other things, for enjoying certain things. An amusing anecdote in the chess world came from retired World Champion Vladimir Kramnik. He recently casually remarked that now that he's retired he's spending less than 50% of his time with chess, as if as if he was just kicking back and neglecting the game by only dedicating 40% of his life to it.
Obviously there are some genetic factors like the ability to visualize/concentrate/etc that people usually think they are talking about when referring to talent. But the role those play will only start to matter when people reach some level at least vaguely approaching their potential, but they'll never get anywhere near that level without the thousands of hours of work and training that they'll likely never complete without a love of that work itself.
This is probably just a really long-winded way of repeating Thomas Edison, "Genius is 1% inspiration, 99% perspiration." The only catch is whether you have the capacity to put out that 99% perspiration.