Measuring current to detect when the battery is fully charged:
In normal (old age) battery chargers there will be the Ammeter connected in series between the battery and the battery charger.
When the battery is almost full. The current will gradually descend near zero. Because both voltages are almost the same. Until the current flows less.
Due to the V = IR rule, if the charging voltage V increases. It will cause the charging current (I)to decrease.
In modern battery charging circuits, The battery voltage will be measured. When the voltage is indicated that the battery is fully charged. The system will automatically cut off the power more convenient.