If you take the Roman Empire as a criterion or scale for an empire and/or kingdom then the Sasanian
king of kings was of course ruling over an empire and therefore he was more an emperor than a king.
But that's pure terminology concerning the emphasis of a country.
The ancient macedionians had a king - called Basileios. But Basileios means not exactly the same like "king". The translation for that is something like "
sovereign".
The East Roman Empire of the Middle Ages has called the ruler
Basileius (beside August
os - a term which was still valid).
But we know that the term Basileios was used to define the emperor - therefore the Basileios (the sovereign) was ruling over an empire.
The chinese title of emperor is
Huangdi (and the "di" means a godhood; therefore the chinese definition was more something like a God Emperor) and is basically just a replacement of the former word "king" - with a drastically increased weightage.
The translation of the first emperor
Shi Huangdi means the first "revered one" (something like "Augustus"). My wife is from China and when she speaks about the chinese emperors she always use the word "king" or "König" (german).
It is also interesting to check the definition of the Romans concerning the sasanian rulers.
They called them "Rex Regum" (which means in english king of kings or in german Großkönig) - the greek speaking Romans of the medieval said "ho megas basileus" or "basileus tōn basiléōn" - the
biggest sovereign.
In my opinion the Roman translations (greek as well as latin) are still the most authentic if we compare it with the original term used by the persians
āhān āh.
Actually it was the land of the "king of kings" and therefore it was a kingdom (or a
āh-dom ).
It was a kingdom which was de facto an empire - the land of an almighty sovereign ruling over many nations and gentiles
.