The earliest 88mm AP shell was just called Pzgr. Patr. for Panzergranate Patronen meaning armor piercing cartridge. (Often listed as just Pzgr.) This went out to the 88mm Flak guns. The velocity of this was about 810m/sec. The round was moderately accurate.
Next big improvement seems to have coincided with the introduction of the Tiger I. The Pzgr Patr 39 was a heavier shell with a small burster. Improved armor penetration and only a muzzle velocity of 773 m/s but was a very accurate round.
There was major leap later to a higher velocity round of 800m/sec. The penetration improved with the increase in velocity again. The accuracy was to become less importance than it's penetration ability as this was less accurate even than the Pzgr Patr.
The listing at Aberdeen says the Tiger gun as having 810m/sec velocity. That may be the same shell as listed under the late Flak 88mm or they use data from the Pzgr. Patr. Or it could be another variant cartridge.
Here is an image from an 88mm/L56 Datenbatten. On the right there are four Pzgr.Patr. 39 subtypes listed. They may be experimental or just steps in the evolution of the shell.
(Someone whose hand this past through drew some big ugly red lines around the HEAT round data. It wasn't me.)
