If you run a current "backwards" through a battery, it charges the battery (though some do not respond very well to this operation).  Start with a good, but completely discharged, car battery, and it will have a voltage of zero.  With a tiny bit of charge, the voltage rapidly becomes 12.6 volts.

Continue charging the battery for a while, remove the charger, and you'll still read 12.6 volts.  In fact, the battery voltage is always 12.6 volts until it becomes fully charged, at which time the voltage rises to somewhere between 13.5 V and 14 V.

An older battery has the same characteristics, but the transition to higher voltage occurs with less charge in the battery.  A new battery may hold 60 ampere-hours of charge, and an old one may hold only (say) 10 ampere-hours.

The voltage regulator has the job of keeping the voltage constant despite changes in engine RPM and current drain through headlights and other power-consuming devices.  Set to hold about 13.5 volts, the voltage regulator guarantees that the battery will be charged any time the voltage is below 13.5 volts, and that means that the charging quits only when the battery is fully charged.