How does USB-C manage to handle much higher power currents?
Part of the answer is more wires, and part is the ability to change voltage also. As for the wires, there are four pairs of power lines in the USB C connector, meaning that there are parallel current paths through several copper strands. This allows for lower resistance and higher current flow. The second part is what they call USB Power Delivery, which has a protocol that allows the power supply and device under charge to communicate with each other (via pins on the USB-C connector), such that the device can ask for greater voltage. Legacy USB devices have only 5V capability, but USB PD adds 9, 15 and 20 Volts. Because power = V x I (voltage x current) you can increase delivered power by increasing voltage or current or both, and this is what USB PD can do. In fact, increasing voltage is a better way to go, because wires do not have zero resistance, and therefore some voltage is lost across the cable (and wastes energy as heat). If the voltage of the source is higher, then a smaller proportion of the voltage is lost in the cable, and this is more efficient. PD can offer up to 20 Volts and up to 5 Amps, there 20 x 5 = 100 Watts. Note that legacy USB devices do not benefit from USB PD, as they are unable to negotiate with a PD power supply and ask for higher voltages, so they will continue to see 5V at up to 2 Amps. This also means the system is backward compatible, and will not drive 20V into a 5V device, which would certainly overload and destroy the device.