No, there are not two different PAPs. The layouts that say "the pin is X distance from the PAP and the CG is Y distance from the PAP" is simply how the driller chose to lay it out. They are the same.
You find your PAP one of several ways. You can use a piece of tape and a low-flaring ball. Put the tape where you think your PAP is. Throw it. If the tape looks stationary in the first 10-15 feet, it's on your PAP. If not, move it and try again. You could also throw a low-flaring ball, arrange it on a spinner so that the first oil track doesn't wobble (i.e., it's on the equator), and for righties with the right of the grip facing up, the north pole is your PAP. You can use an Armadillo as well. The accuracy of any or all of those methods is slightly debatable, and will depend on just how little flare the ball gets. A ball with no flare should be the most accurate. Your PAP is then declared to be a certain distance from the center of grip and so far above or below the midline.
Once you have the PAP, and you want to drill a ball with, for instance, a 4x3 layout (4" pin-to-PAP, 3" CG-to-PAP), draw a circle around the pin with a radius of 4". Do the same with the CG. One of the places they intersect will be the spot you call your PAP (the other intersection will be in a wonky spot). Using the distance from the center-of-grip to your PAP on the other ball, back out where the center-of-grip will be on the new ball.
Summary: You find where the PAP is in relation to the center of grip on an existing ball. Then you choose the layout you want (you can also do degrees for the CG/MB instead of some specific distance, and there's a vid of a Big B staffer laying out a Zone Classic like that). The layout will tell you the spot that has to be the PAP on the new ball. Then you back out where to put the finger and thumb so that that spot actually is the PAP.
SH