You're absolutely correct tmcase. The 'thing' or variable that is adjusted is always the voltage.
The difference is that when you set volts, the PV will give you that voltage to the best of it's ability with no regard to anything else.
When you set watts, the PV will check the coil resistance and then set the voltage to make the watts (power) you selected. Change the coil to a different resistance and the PV it will change voltage to keep the watts constant.
The PV uses only the mode it is set to. So if it's set to VV, it completely ignores what is set on the VW screen and the same the other way around.