The term "Byzantine Empire" is a term generated by historians to distinguish that period of the Eastern Roman Empire (which its citizens thought of themselves as inhabiting) from earlier incarnations where Rome remained the capital. After the fall of Rome in the 5th century AD, the capital of the empire moved permanently to Constantinople, formerly called Byzantium, and it's here that historians begin to refer to the separate Byzantine Empire. Citizens of the Byzantine Empire would have continued to conceive of themselves as inheritors of the Roman Empire's legacy.

Meanwhile, in Western Europe, the fall of Rome (actually, the decline and multiple falls of Rome - the city was sacked multiple times, contrary to popular belief) was fairly cataclysmic for the European worldview. Rome retained a lingering sense of legitimacy and strong centralized power that wouldn't really be seen again on a continental scale in Europe until the Napoleonic wars. As a result, even three centuries after Alaric took Rome, the idea of a central "Roman Empire" still had significant cache of almost mythical proportions, which is what made the coronation of Charlemagne such a momentous event. With Charlemagne's Holy Roman Empire, Western Europe had - in theory, if not in practice - a successor to the glories of ancient Rome, with the authority and the prestige that accompanied them. Though the term "Holy Roman Empire" itself came centuries later, Charlemagne and Otto I definitely used the imperial grandeur of Rome to legitimize their claims to dominion over their massive territories.