Piebald is a condition where random patches on the skin/fur/scales that have no pigment. It doesn't show up in a specific location, and it can occur in few or many patches of varying size pretty much anywhere on the body.
It is likely completely separate from a "marble" where it's blue with black spots or white spots or something like that. It is lack of color in these patches entirely.
Don't get sucked in with the random names people decide to use to sell their fish. Piebald is a genuine documented condition.
Now, i'm not aware of there being 100% proof that the piebald condition exists in Bettas, but it certainly looks like it does. While most of the likely examples i've seen have the "patch" covering at least some of the head, it's not the only way it can present. I have seen it where the patch/ patches are on the body somewhere and the head is colored.
In the rest of the animal kingdom, piebald is a recessive trait. If it is Pibaldism in bettas, it is most likely also recessive and should not appear in in subsequent generations unless both parents were carriers. Again, bettas have extremely varied genetic backgrounds so many may carry the gene, it's hard to know unless they display the trait.