What was the difference between emperors/empires and kings/kingdoms?

Simply put, a kingdom is any state headed by a single monarch, the King. An empire controls multiple groups of peoples, and if it is headed by a single leader, that leader is the emperor. To relate to very early states, Ancient Egypt was a kingdom due to being headed by a single monarch (pharaoh), but in later time periods it's often referred to as an empire because the kingdom extended its control to neighboring societies and peoples to the south and in Canaan. Of course, this is just the basic understanding. Throughout history the terms have been used in different contexts, and often overlap. Less ancient example, the Second Reich. The Kingdom of Prussia united the other kingdoms and republics of Germany into one empire. The King of Prussia assumed the position of Emperor of Germany, while maintaining his older position as well (the Empire maintained a system of semi autonomous states within, as I understand it). The term "empire" was used despite the entire state being concentrated around one national group of people. Just an interesting example of the different uses and overlaps of Kingdom and Empire.