An Emperor is the highest power in the region he occupies and for most practical purposes they were in a world of their own [Emperors of China, India, Persia and others have often seen themselves as the rulers of the world]. If there is a bigger power in the vicinity [whether political or religious], it would be silly to call him an emperor. Kings are not necessarily the biggest powers and they often pay tributes to other powers [emperors, pope or other kings]. While the title of King is primarily political, the title of Emperor often makes one the head of the religion too.
While a King rules one fairly homogenous territory [called a nation/kingdom], emperors often wield power over a fairly heterogeneous territory [ruler of many nations]. Persians are usually assumed to have originated the term [Shahanshah - King of Kings] from where others have taken this.
In the ancient/medieval world, Emperors had special significance. Europe for instance had only one Emperor at any point and the control was said to transfer in a quasi linear way
n India, only the Samrat/Chakravartin can perform the Rajasuya sacrifice.
In the past, there would also be specific priority as a part of protocol that would treat an emperor different from the kings. In the modern day the term has been abused enough to render the difference meaningless.
