While the Roman emperors attached "Caesar" to their names and eventually they were frequently referred as the current "Caesar", the official title of their function was "imperator", hence "emperor".

Julius Caesar has refused the title "imperator", for reasons of public image, even if de facto he had the same power as an "imperator", i.e. the power to give commands that must be obeyed by anyone else.

All his successors possessed the title of "imperator", so they are correctly referred as Roman "emperors".