Too complex for a simple answer.
The answer varies with battery chemistry.
The charger manufacturer chooses the method right for the cell concerned and implements electronics to suit.
Some batteries can be charged to a setpoint voltage.
eg LiFePO4 at high charge rates.
Some, like LiIon, and LiFePO4 at lower charge rates [and lead-acid in some cases (as Joe Hass says)] are 1st charged to a set voltage at constant current and then at constant voltage until current reduces to some % of max charge rate.
Some (eg NimH, NiCd) use detection of a DROP in terminal voltage at a given current (negative delta V) as full charge is reached, or rate of temperature rise (delta T).