Hi Borek,
If you like, the terms can be changed from positive charge electrode to electrolytic anode and negative charged electrode to electrolytic cathode.
Think of charging a regular capacitor. If you charge a capacitor to 2V then the positive plate gets +1V and the negative plate gets...
For an electrolytic cell, the voltage source Vs, does not contribute directly to the potential on the electrolytic electrodes. Vs determines the current and can add charges to the electrodes. This can be observed when charging supercapacitors and is discussed in these threads ...
What is the F/cm^2 for a commercially available supercapacitor? Much of the literature is on newer types of carbon, such as graphene, but are commercially available supercapacitors based on activated carbon?
http://www.pnas.org/content/suppl/2015/03/22/1420398112.DCSupplemental
In this article...