20+4-pin PSUs are designed that way specifically to allow compatibility with both 20-pin and 24-pin mainboards. The 4 extra pins simply carry extra voltage wires and a ground wire because 24-pin mainboards are supplying more power to hungrier components. A 20+4 PSU is functionally the same as a 24-pin PSU, it's just modular.
Just in case you might be confused though, the extra 4 pins on a 24-pin socket are NOT the same as the +12V connector introduced with the Pentium4. That connector has 2 12V wires and 2 ground wires (2 yellow, 2 black usually), and the connector has a clip. If your PSU has a 20-pin ATX connector and the +12V connector, it is not a 20+4-pin PSU. It sounds vaguely like this might be what you were thinking about.
SocketAM2 mainboards require both the 20+4 ATX connector (the extra 4 pins are usually modular so that you can use it on an older 20-pin board, but they are still strapped together with the rest of the ATX power wires) as well as the +12V connector.
If you're not sure, get the exact model number of your PSU and we can see what connectors it actually has.