We will discuss the later Roman Empire, with emphasis on the regions that are now Turkiye (Turkey). The numismatics can be conveniently divided into two periods: that of the Tetrarchies, and then from Constantine to the split of the West from the East.
The West, as of 476 A.D., basically told the East: “We’re cool here. We’re going to stop asking you for stuff and we’re not going to give you stuff either. You can keep being the emperor, that’s fine. Just don’t try to get us to do anything.” Or put another way, in reference to the political issues of the day, the West declined to help the East deal with Persia. The emperor, in Constantinople, said “OK,” being in no position to do anything to keep the West from walking out the door.
Twenty years later they had an administrative reform in the East and began the phase that we call the Byzantine Empire, but which they continued to call the Roman Empire. The West became the domain of (only technically) vassal “barbarian” Kings.
The emperor, in the East, could and did sometimes, grant an Imperial Charter to a Western King. Propaganda point, or not, didn’t matter. They also invaded and occupied parts of the West from time to time, but nothing permanent. The Western Kings did what they wanted to do after 476 A.D.
Back to the Tetrarchies, two centuries earlier, there was an attempt to keep
