Welcome to the AT forums if I haven't done so yet.
You can go to
formfactors.org to read the current ATX spec and view the change-log (right at the beginning of each version of the spec). I think the main change between 2.0 and 2.2 is the complete dropping of the -5V rail which nothing uses anymore anyway. (The -12V rail won't be around much longer either.) And they added a few more connector types and increased the current rating for the contacts in the P4-12V connector and the ATX connector. They standardized on the 24-pin ATX connector in the ATX 2.0 spec.
. About the only thing you'll need to check if your mobo still has the 20-pin ATX connector is that the PSU has the 4-pin part that you can split from the 20-pin part as the 2.0 spec made the 24-pin EATX (aka EPS-12V) connector the standard. Or if your mobo has some room off the end of the ATX socket opposite from the orange wires, then you could use a solid 24-pin connector and just let the extra 4 pins hang over the end of the socket. That's what I do. Worse-to-worse you could just get a 24 to 20 pin adapter - some PSUs with solid 24-pin connectors come with the adapter, but it is always best to avoid adapters in high current circuits if at all possible.
IAC, an ATX 2.2 PSU will work fine - if you had mentioned make and model of your mobo, I could be more sure - but I'm over 95% sure without the info.
.b.h.