Theodosius I nominated his two sons for a co-emperorship: Arcadius (the elder one) in the east, and Honorious in the west.
The Romans only used one term: Roman Empire. The terms Western Roman Empire and Eastern Roman Empire have been coined by historians. Historians have also coined the term Byzantine empire for the Eastern Roman Empire after the fall of the Western Roman Empire. Therefore, this term applies to a period that started 81 years after the death Theodosius.
Historians also put the death Theodosius at the time when they consider the two parts of the empire as becoming split. This was not due to an official act. It was down to circumstances. His two sons were young and incompetent. This allowed powerful men in the courts of the east and west to conspire against each other. In addition, the fall of the west started soon after with the first wave of Germanic invasions in the west, which occurred 11 years after Theodosius died.
The Eastern Roman Empire. It became the Byzantine empire after the collapse of the Western Roman Empire.
The Western Roman Empire and the Eastern Roman (Byzantine) Empire.
The eastern half of the Roman Empire became the Byzantine Empire.
Byzantine Empire
The Eastern Empire was mostly abandoned because Threats from outsiders, became too big to control, and something else. So since the people above the Roman Empire started attacking the Eastern Empire, they moved to the Western Empire. Diocletian (Or someone like that..) Divided Rome into the Eastern and Western Empire.
The Eastern Roman Empire. It became the Byzantine empire after the collapse of the Western Roman Empire.
Western Europe (Eastern part of the Roman Empire did not collapse and became known as the Byzantine Empire) went into a period of chaos, then arose in the feudal society (Middle Ages)
Milan in the Western Empire and Byzantium in the Eastern Empire.
The Western Roman Empire and the Eastern Roman (Byzantine) Empire.
The eastern half of the Roman Empire became the Byzantine Empire.
All of the western lands of the old empire became part of the Byzantine Empire.
All of the western lands of the old empire became part of the Byzantine Empire.
The eastern part of the Roman Empire became what remained the Roman Empire after the fall of the western part of this empire in the 5th century. Historians use the term Byzantine empire to indicate the eastern part after the fall of the western part. However, the people in question did not know this term, called their empire Roman Empire and considered it to be the Roman Empire.
Byzantine Empire
The Eastern Empire was mostly abandoned because Threats from outsiders, became too big to control, and something else. So since the people above the Roman Empire started attacking the Eastern Empire, they moved to the Western Empire. Diocletian (Or someone like that..) Divided Rome into the Eastern and Western Empire.
The eastern part of the empire became known as the Byzantine.
The Byzantines were the inheritors of Rome. After Roman Empire split, Eastern Rome became known as the Byzantine empire, after the capital city of Byzantium. The Eastern Empire would outlast Western Rome by centuries.