Can't be done in your second scenario. All you can do is charge another battery from a charger and swap out the discharged one.
Otherwise you need to have a charger imposed between the two batteries, and use a SMPS (less 10-30% for losses) so it can step the voltage up if the charging battery has the same nominal voltage, but it will need a higher capacity.
Using a SMPS, it is also possible to have batteries with terminal voltages above or below the terminal voltage of the battery being charged, and with a higher capacity battery you will be able to charge a number of lower capacity batteries. (eg, use a big 6V lead acid battery, which will need less frequent charging). Can't see any of this is much use unless you have a situation where you have a lot of low power remote devices, with fixed internal batteries, and there is no power, either wired, solar, or portable generator, nearby. Means you have to lug a large battery and charger around and have to hang around at each location while the battery charges.
Cheers,
Richard
