I believe that the extra connection is for the power supply fan.
In the case of the 2 wire version, I suspect it is a tachometer to monitor the speed of the power supply fan.
I think the 3 wire version is a version which would allow control of the power supply fan (2 of the wires) and also monitor the speed (the third wire).
I would hope that the fan in the power supply runs regardless of the 3 wire version being connected: you can safely test it by switching on for a couple of seconds to see if the fan runs. If it does then you are OK, if it doesnt then switch off immediately before any excess heat builds in the power supply.
As an alternative to my guesses, is there no information with the power supply to tell you? Or can you get info from the net (if necessary using another computer) to find a data sheet?