This is my understanding - it may not be correct.
An injector is basically a hole that is open or closed. The rate at which fuel passes through this hole is governed by the pressure differential either side of the hole (ie higher DP = more flow, lower DP = less flow). The amount of fuel entering the engine is controlled by the length of time the injector is open (ie higher Dt = more fuel, lower Dt = less fuel).
The ECU controls the length of time the injector is open and the fuel regulator controls the pressure differential. In a turbo car the regulator raises the fuel pressure with boost so the DP across the injectors is constant. Any excess fuel is returned back to the tank.
A fuel pump has a curve which relates its flow and pressure. Typically as pressure increases flow decreases. An engine will requires a certain max flow at a certain max pressure. The pressure is set by the reg and the pump is designed to meet this duty.
If you start increasing power, the fuel flow and pressure requirement from the engine changes. If the pump cannot meet the flow requirement the fuel pressure drops, less fuel is injected and the engine leans out - which is sometimes fatal.