What do AP #s (or stars) correlate to?

Casks?
Vineyard Plots?
Something else?

All and none of the above. It depends on the winery.

Officially the AP number refers to the wine as it was submitted for its official analysis/tasting review. A producer may submit a sample from a single fuder (cask) or tank, or a sample that comes from a final blend of several fuders/tanks. So (to give an example) when J. J. Prum releases a 2005 Wehlener Sonnenuhr Auslese that has an AP number finishing with 23-06, it means that was the 23rd wine they submitted for approval in 2006. Whether that was a single cask of Riesling or a blend of several nobody will know since Prum does not allow folks into the cellars. In some other cases, producers like Schmitt-Wagner, Merkelbach and Muller-Catoir submitted samples from single casks for AP numbers, and sometimes (e.g. Catoir in the past) that cask number (not so much a cask but rather a sequential number of hte wines made by the estate, but cask is close enough) also showed up on the label. Thus in 2001 we had 2 Catoir Haardter Burgergarten Riesling Spatlese in the USA, one with 2133 in the upper right hand corner of the label and the other with 2134 - each having it’s own distinct AP number (I think 2134 was AP#9, but can’t be certain without a bottle in front of me - or a frontal lobotomy).

Stars? My God, it’s full of stars.

Just to be entirely anal about it, that '01 Catoir 2134 was a special bottling exclusively from the Breumel.

Thanks for fielding the query.

Thanks David.

What is a Breumel?

Sub-parcel of the Haardter Burgergarten.