Isn't this just a conceptual thing? It's still the electrons that are moving, and they're leaving "holes" behind so you can model either the electrons moving or the holes moving but there's still only one particle.

I agree with the top parent comment, I wish we had gotten the charge of electrons correct. I remember bandgap diagrams being confusing too because electrons basically roll "uphill" and felt like it would be easier to understand if we just called them positive.

In P-type semiconductors, a small amount of impurity/doping produces "holes": http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/dope.html#...

Free electrons can temporarily occupy holes, then dislodge themselves and move on to the next place. But it will look like as if the holes are moving from one place to another.

You can have positive ions in liquids, like in a battery.

They don't in metals but I don't think it would make any difference if they did.