I'm not sure if anyone ever gave you an answer on your question/issue but I might be able to shed some light what I THINK is going on as I'm a recovering electronics engineer albeit a bit rusty. This is just a hunch.....

There are many ways to characterize and quantify AC waveforms (peak to peak, max amplitude, RMS root mean square, etc.). Generally speaking, RMS takes wave shape into account and gives an indication of the amount of "power" in a waveform. Something you are already familiar with are your AC power mains, 110 or 120 volts in the US (or 220V). That figure is 120/220 volts AC (alternating current) RMS. If you would look at the waveform on an oscilloscope you would see it is actually a peak to peak sine wave approximately +/-170 volts. The conversion from pk-to-pk to RMS is multiply by 0.707

Looking at the welder, the 325 amp capability is probably describing the peak to peak voltage. If that's the case, a 325A sine wave has an RMS of 325 times 0.707 or 230 which is pretty darn close to your observed 220.

Similarly the conversion of a square wave from pk-to-pk to RMS is one. That is, the numbers are the same which is again close to what you have.
I'm guessing that a triangle waveform's conversion is 1/2 or in this case approximately 162A
Soft-square is not a mathematically meaningful waveform so God only knows what the conversion would be.

My guess is that the welder's electronics is measuring RMS.

Hope this helps.