Sorry, that was bad writing on my part. I meant that this was the distinction. In Byzantine history, transitions between one sovereign to another always consist

Sorry, that was bad writing on my part. I meant that this was the distinction. In Byzantine history, transitions between one sovereign to another always consisted of a new sovereign seizing the control of the Roman state. In the example of Charlemagne or the Turks or whatever, it's a non-roman state that replaces (or in their eyes, becomes) the roman one, rather than just a non-roman sovereign.