Paying one will not pay for the other.
Drivers using the Dartford Crossing need to pay the Dart Charge in advance or by midnight the day after crossing. Pay online or by phone, post or at retail outlets. It is still free to use the crossing 22:00 to 06:00.
Unlike the Dart Charge, you can't pay Congestion Charge at retail outlets. See Paying the Congestion Charge.