Well, I am unsure what term Anglophones use when talking about the German thingies.
In English, the whole area was called the Holy Roman Empire, even though it was neither Holy nor Roman. The ecclesiastical states in the Holy Roman Empire are referred to as either bishoprics or archbishoprics, as appropriate. Some of the smaller ones, like Weingarten, we call abbeys or provostries, if it's just a monastery surrounded by farmland, or an Imperial City if it's bigger, like Rottweil. (Mostly we just know about Rottweil for their dogs, which are very popular among the mulleted crowd in Pennsylvania.)
The ecclesiastical states on the Italian peninsula, prior to unification, were called Papal States in English-language gazetteers (and Pontifical States in some early U.S. Atlases).