Charging a battery with more mA than its genuine charger
The "charger" is actually a battery management IC inside the smart phone.  Assuming your phone uses a Li-Poly battery, the battery will be rated at a nominal voltage of 3.7v and a fully-charged voltage of 4.2v or thereabouts.

The battery capacity of a LI-Poly battery in a smartphone is rated in mAh, and a typically value might be 1300 mAh. The charge rate is often denoted as C and signifies a charge rate equal to the capacity of a battery in one hour.  For a 1300 mAh battery, C = 1300 mA.

The charging current is typically set externally to the charger chip using a couple of resistors.  Values of 0.5C (650 mA in this case), 0.8C and 1C are common.  A rate of 2C (2600 mA or 2.6A) would be classified as a fast charge.

Sometimes the resistor network can be adjusted by the microcontroller inside the phone, so it can set the charging current to either 100 mA or 500 mA when connected to a regular USB port, or to a higher value (e.g. 1C) when connected to an AC adapter, colloquially known as "wall-warts".

These AC adapters are not chargers, but simply AC to DC converters.  The current available for charging will be limited by the output of the converter (i.e. if it supply 1A, the charger chip cannot charge the battery more than 1A), but if you replace a lower current wal-wart with a higher one, then the battery might be charged faster, however the charging current will still be limited by the charger chip -- whichever is lower, the AC adapter capacity or the charger chip setting.