The differential is a number that tells you something about the internal weight distribution of the ball, and it is only indirectly connected with the PAP through the layout of the ball. It tells you something about the core and the ball's internal weight distribution.
"Mid differential" is normally the core's average RG number (the middle between RG min. and RG max., the calculated "points" on the pin axis where the core has its largest difference of weight distributions - pretty abstract), some manufacturers list the mid diff. as an RG number, others list min. and max. The RG differential is the difference between RG min. and max., and it is an indicator how much flare potential a ball has through its core's properties.
How much of this potential is actually tapped depends on the relative position of the pin to the user's PAP (plus some other factors).
Hope that helps?
