An as far as I know explanation about Samsung's charger and cable
Samsung's modifications for fast charging are only applied on the charger, the data pins of the charger's USB output ... and yes, the Samsung charger has enough power.
The Samsung cable isn't modified, it has the four power and data wires like a standard microUSB cable. And
its power wires have the right gauge (low resistance in relation to the cable lenght
) to ensure a proper amperage flow while charging.
BTW, some generic chargers have applied part of Samsung's modification ... jumpered data pins on their USB outputs. And some phone manufacturer's chargers have it too ... HTC charger's have it I know for sure.
But Samsung's charger additionally set a voltage level of 1.2V on the jumpered data pins.
This could explain different charging times:
Without jumpered data pins -> trickle charging (with an amperage up to 500mA).
With jumpered data pins -> fast charging.
With Samsung's mod -> faster charging (for Samsung devices).