PCI 2.2 is the traditional 32-bit, 33Mhz PCI bus. When you see a device or slot referred to as PCI, that means it’s normal PCI 32/33. 64-bit PCI slots and devices exist, but only on server and other very high-end motherboards. In the end, PCI-Express will replace PCI, its variants, and AGP in the coming year or so.
Also worth mentioning is that PCI 2.2 is not that different from PCI 2.1. AFAIR the only difference is that 5V signaling is no longer supported.
PCI-X is an extension of PCI, using the same physical conectors, but slightly different signalling, to ensure a higher throughput (at the expense of a slightly higher latency, although that’s compensated for by the increased frequency). It’s still backwards compatible though. You can take your old 32-bit PCI sound card and plug it in your 64-bit PCI-X slot.
I have never even heard of 533MHz PCI-X, but I suppose I should cease to be surprised when they increase the frequency. (I can’t understand how they manage to keep all the bits synchronized at that speed though. I thought that’s why intel is trying to push 3GIO (nowadays called PCI-Express), which is a serial bus.)