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I think the best way to answer your question is to try an example. Let’s calculate the gain using all 3 of the voltage types that you mentioned. The first one will be arbitrary numbers. The other two will be based off the first one.
For RMS let’s arbitrarily assume that we have 10 volts out and 1 volt in. That would make our gain = Vout/Vin = 10/1 = 10. So we have a gain of 10.
Now for peak voltage we need to take our RMS voltages and convert them. To convert the 10 volts RMS we would have Vpeak = (Vrms)(1.414) = (10)(1.414) = 14.14Vpeak. To convert the 1 volt RMS we would have Vpeak = (Vrms)(1.414) = (1)(1.414) = 1.414Vpeak. Now to calculate our gain using peak voltages we would have Vout/Vin = 14.14/1.414 = 10. So we have a gain of 10.
Now let’s try peak-to-peak voltages. We will need to convert our peak voltages to peak-to-peak. To convert the 14.14Vpeak we would have Vpp = (Vp)(2) = (14.14)(2) = 28.28Vpp. To convert the 1.414Vpeak we would have Vpp = (Vp)(2) = (1.414)(2) = 2.828Vpp. Now to calculate our gain using peak-to-peak voltages we would have Vout/Vin = 28.28/2.828 = 10. So we have a gain of 10.
So as long as you use the same kind of voltage for both the output and the input, the gain will come out the same.