One component of the high-pressure fuel system is the fuel pump. It raises the fuel pressure until it reaches the pressure required in the rail, which is necessary for the injectors. It should be noted these pumps have a low-pressure part and a high-pressure part in addition to the FVR (Fuel Volume Regulator), which controls the pressure.
The OBDII DTC P0003 is related to the electrical part of the fuel regulator system. It is set due to the electrical reading being lower than expected.