Nowadays, the OE wheels on designed to pilot on the center hub which basically solves the problem of the wheel being centered. This is not always true for aftermarket wheels which require a hub ring to properly center the wheel.
But aside from balance there is "out of round" - or more techncally "uniformity" - that affects the vibrational characteristics of a tire (and wheel). Many tire shops are still using balancers that only do balance - and most of the time that is adequate. But the more up to date shops use the Hunter GSP97000 which also measures loaded run out and that machine will solve nearly all vibrational problems.
However, from time to time, the other rotating components at the wheel end - rotors, hub, etc - will have a balance problem that those machines will not address. This is where the on-car balance comes in.
But as has been pointed out, moving the tires (and wheels) will change things and the vibration will resurface.