The fuel pump get power for a couple of seconds when the starter button is pressed, and get continous power when the engine is turning (when the ignition ECU receive signal from the hall sensors.
The fuel injection relay deliver power to the fuel pump and other this and that in the FI system.
(injectors. AFM, TPS, FI ECU).
The FI relay get its signal from the ignition ECU at the ground side of the relay coil.
When you push the button, or the engine is turning...ignition ECU grounds the relay coil...the relay closing the contacts and deliver power to the fuel pump + this and that.