Imperium Romanorum is the translation of the official name of the Eastern Roman Empire in Latin ie Basileia Romaion. After Heraclius the Hellenized East translated the Latin title of Augustus Imperator into Basileus. However after the coronation of Charlemagne as Augustus Imperator the Basileus became a focal point between the two empires of the old East and the new West. In order to strengthen the fact that the only true Roman Emperors were the incumbents of the Throne in Constantinople and not in Aachen they used the title Basileus Romaion and for the state Basileia Romaion thus Imperium Romanorum.
Now the Empire was split by Theodosius the Great in two parts for his sons each one centered around Rome and Constantinople respectively. In historical sense when you say Imperium Romanum you refer to the Roman Empire as a historical fact till the fall of both its parts ie till 476 AD for the West and till 1453 for the East. When you are using Imperium Romanorum then you are exclusively referring to the Eastern Roman Empire as a state from the foundation of Constantinople in 330 AD til its fall in 1453 AD.
