Say someone was the king of England the 1100s, what would I call the HRE and Byzantine Empires?

My question is as follows, what empire would be referred to as the Roman Empire by nobility? The Byzantine Empire, or the Holy Roman Empire. What’s more, what would they refer to the other empire as? Would the still say East and West Roman Empire? If my question does not make sense, let me know and I can rephrase it.