While they do, I would make the suggestion that the puppet cities reflect more closely autonomous cities within an Empire. Such cities have existed throughout history, but are learned most commonly with the Holy Roman Empire (however, Tyre was such an example in the Assyrian Empire, for example).
However, you are right. From a name perspective, it might be too difficult to draw the distinction. However, I have a modest suggestion in the subforum that uses City-States to reflect vassals. It is essentially a puppet leader, however, so perhaps I'm blending them together too much as well.