With different cell ratings you have to expect a different time for charging, which changes the 20, 40, 60, etc., points.
For example, with a cell rated at 2 ampere hours that's 120 ampere minutes, so 24 ampere minutes means 20 percent charged. But for a cell rated at 1 ampere hour that's only 60 ampere minutes so 12 ampere minutes means 20 percent charged.
The charging circuit in the phone uses USB 5V as its power supply. A single Li-Ion battery cell charges at up to 1C (its mAh current rating) and when its voltage reaches a maximum of 4.20V then its current slowly decreases as shown on the graph I posted. When the charging current becomes very low then the charger circuit disconnects the charging. The charger circuit also disconnects the load when the battery voltage drops to about 3.2V.