i'm not an engineer either but have 16 years in refining with MANY associated classes in the mechanics of fluids. i've worked with tons of different fluid systems including pumps you could hold in your hand up to 11,000HP turbines and fluids from electrolytic hydrogen to asphalt. in a given system all else being equal a higher pressure differential equals a higher flow, that's how it works. generally speaking in an engine the low side of the equation is basically set by the clearances, the high side by the relief in the pump. as pressure increases (thereby increasing differential) flow increases that's how it works. these are the very basic principals of the mechanics of fluids and i really wish i was better at explaining them because they come up so often.

take the three different pumps normally used. standard, high pressure and high volume. the standard and high pressure pumps are normally the same pump the only difference being the relief spring, the high volume pump has bigger rotors. if the standard pump and high volume pump both have the same relief spring in them (say 60#) and they both develop 60# of oil pressure (both hitting the relief pressure) on the same engine then they are BOTH pumping the SAME volume of oil through the engine. if you put the high pressure pump on the engine with say a 70# relief spring in it and the engine builds 70# then it is pumping MORE oil through the engine than BOTH of the other pumps. all else being equal higher pressure means a higher volume of oil is being pumped through the engine.