Yeah it's definitely not very clear. I did a lot of research on this last year to put together
my guide. Basically the US sport package prior to 09/01 had Sachs Advantage dampers, which are the same dampers as what MSport had in Europe. The ZHP got Super Touring dampers from day one (confirmed by ZHP owners who still had their original dampers), which are softer than Advantage. However, after 09/01, Advantage wasn't offered in the US anymore at all (there were a lot of automotive journalists who complained that the sport package was too stiff), and all sport packages and ZHPs received Super Touring dampers from then on. You can trace the lineage back by cross-referencing the original BMW part numbers (
from BMW ETK) with the corresponding Sachs part numbers from the
ZF catalogue (this is what I did for my guide).
This would make sense for the ZHP since it is designed exclusively for the US market which has worse roads, so the person who put together the package (a man that goes by the name of Richard Brekus) probably chose the Super Touring dampers over Advantage for better ride quality on US roads. The information about the ZHP having stiffer shocks comes from the marketing department which I personally would not trust. I trust part numbers more.