Ok, I'm no EE but I will try to explain this voltage relationship in a fairly simple manner.
Using the KGSS design as a reference point, we will start with the
power supply output which is
+350 volts DC and -350 volts DC referenced to 0 volts (ground).
So here we have a total direct current (DC) "voltage swing" potential of 700 volts.
These voltages, +350 and -350 are connected to the amplifier board.
We use the term "rails" to denote the individual "voltage highways"
that the positive and negative voltages travel on. Some use the term "buss" instead.
Inside of the amplifier board is where all of the voltage transformation magic occurs.
The DC voltages from the power supply are turned into "quasi AC voltages"
that conform to the audio signal that is applied to the amplifier input terminals.
The amplifier's job is to magnify the small (~2V) audio input signal, then output it to the headphones.
The KGSS employs four "gain stages" to do this along with a volume control that "attenuates"
or cuts back on the maximum possible gain to control the outputted level to something that is comfortable for listening.
For more reading on the KGSS theory of operation, please click on the following link and read "How it works":
http://gilmore2.chem.northwestern.edu/projects/showfile.php?file=gilmore2_prj.htm
Getting back to the "quasi AC voltages" mentioned above,
The small two volt audio signal (from the source) is an alternating current (AC) voltage, also known as a varying sinusoidal waveform. (sine wave)
Inside the amplifier, this low voltage AC audio input is superimposed over the DC high voltage that has been fed in from the power supply,
thus magnifying the AC input signal and turning the DC rail voltages into a "quasi AC" output voltage in the process.
This is where the concept of RMS and peak to peak (p-p) voltages comes into play, expressing the maximum peak potential for these varying AC sine wave voltage swings.
If one wants to learn about RMS, wiki explains it well:
http://en.wikipedia.org/wiki/Root_mean_square
Suffice it to say that RMS voltage is the part of the AC voltage waveform that actually does the work.
Roughly speaking it comprises the lower 2/3's of the AC waveform,
the "peak voltage" comprises the rest and is of relatively short duration when encountered during extreme amplitude excursions of the audio signal.
Good thing, because if it did persist and packed a "current punch", it would burn out the electrostatic drivers on the headphones.
Stat amps are designed so the RMS rail voltages do not exceed the bias voltage (current Stax = 580VDC bias)
so as to prevent excursions of the diaphram into the stators, as that could cause arcing and burnout.
+350VDC to -350VDC = 700V DC voltage swing at power supply (not to be confused with AC voltage "peak to peak" voltage.)
Therefore ~~~~~~~~~~~700V AC RMS voltage swing inside of the amplifier ~= 1KV AC p-p voltage swing. (full waveform, positive and negative going phases)
FWIW, Stax and most manufacturers reference the DC or AC RMS rail voltages for their products. Not the less meaningful, although greater peak to peak values.
I'm sure that someone will come along to correct me in at least few aspects of my diatribe.
Please note that the concepts above are approximations to get an idea or three across. I have not referenced applicable test frequencies, etc.