“Xibei” just means “Northwest China” = (presumably) “Northwest China Cultivar Group” = all NW tree peony (mudan) cultivars, not just those with a purple blotch in the centre of the flower.
“Ziban” means something like “having a dark centre“; “Ziban mudan” means all peonies with a dark-centred flower, that is, P. rockii and its cultivars. It appears that in traditional Chinese usage there was no special word for P.rockii as a species. Rather each dark-centred cultivar, whether a selection from P. rockii or a cross with another species, was given a special name and categorized as an example of Ziban mudan.
“Gansu mudan” — literally, “tree peonies from Gansu” — are usually understood as a subcategory of Ziban mudan — that is, Gansu mudan are particularly lush, fragrant and beautifulZiban mudan cultivars that originated in Gansu.