The two are directly related, but there is a difference between dissolved carbonation and the pressure at your tap. The amount for carbonation in your beer depends on the pressure and temperature you store your beer at. At 40 F, 9 psi gives about 2.2 volumes of carbonation where as 14 psi is about 2.7 volumes. They give pretty different mouth feels.
The pressure driving flow at your tap is affected by the regulator setting and by the restrictions in your equipment setup - like the height your beer has to travel upwards and the resistance to flow from tubing diameter and length.
Dissolved carbonation is slow changing and not all that affected by your equipment setup as long as no abrupt changes occur. Think of a soda that is open - the carbonation remains for a long time unless you do something that causes the carbonation to instantly desorb, like dropping a mentos into it. This is why low flow and tilting a beer helps keep the beer fizzy and the head from getting too big and why having the flow at the tap too high causes too much foam.
I keep my beers at 40 F and 15 psi - I like them on the fizzier side. I let the stouts warm a bit in the glass before drinking them. I use a tap line that is about 6-7 ft long with a 3/16 inside diameter and about 2 ft of head from the keg to the tap. This gives me a big enough pressure drop on the driving force so foaming is reduced, but I still have a fizzy beer with a nice head.
Your idea of storing at 14 psi and serving at 9 psi effectivley makes up for too little pressure drop in your set up while serving but you have to reset your regulator to 14 psi after you've had your fill or your beer will eventually equilibrate at a less carbonated level.