fuzzybabybunny:
Ok, so I guess this is where using the water analogy breaks down, right?
It's more like a potential energy within a "local" system (or subsystem).....a localised system. In that localised system, if there is a "separation" of charge caused by carrying out the relevant procedures or processes needed to do that (where input energy is involved), then a physical phenomenon is known to occur..... creating an electric field of some sort. So..... like the kingsman II movie..... whatever happens in Italy stays in Italy.
It's only when you connect batteries together in series where the voltages of series-connected batteries become additive (for the equivalent "overall" battery).
Better to think of the value of charge on one terminal of a particular battery "relative to" the value of charge on the other terminal of that particular battery.