If we take as an example, a power supply such as one found in a PC, which takes 110/220v and steps it down to 3.3v/5v/12v. We can usually draw 30 amps from the 12v line with no problems (360 watts of power). But the power supply is connected to an extension cable with a 13 amp fuse.
Therefore, it must be the case that the current on the 110/220v side is not nearly as much as the current on the 12v side.
But how is that possible? If current is a measure of charged particles moving across a point, how can that change by changing the voltage? Is it the case that the higher voltage particles have more "speed" or "energy" so that one of the moving faster can push 3 of the lower voltage particles?