The hole is a quasiparticle, i.e. something that behaves as if, to some extent, there were a particle instead of the system that we are dealing with.
The positron is a real particle, that exists on its own.
The hole only exists in the presence of other electrons, it cannot exists on its own. This is because a hole is the absence of an electron, but the concept of of "absence" only makes sense if there are electrons around. The hole "moves" only because a neighbouring electron fills the vacancy and the hole therefore shifts.
Here's a sketch:

Hopefully from this you can appreciate that the hole can only "exist" and "move" when there are several electrons around, but it could not do it on its own.
A positron can exist and move on its own, it's real.