Learn English – Realm vs Kingdom

Bringing together a couple of good answers, the primary differences between a King and an Emperor are:

• A king rules one "country" or "nation"; an emperor rules over many. This is implicit in the definition of "kingdom" vs "empire"; an empire is always made up of multiple countries that have come under full control of one governing body (typically under one man, sometimes under a small group such as a triumvirate). So, to be an emperor, you have to have an empire; typically you go from "king" to "emperor" by conquering your nearest neighbors.

• A king normally rules by birthright; an emperor normally rules by conquest. Note the use of the word "normally". Kingdoms change hands between ruling families; the British Royal Family count ancestors from several formerly-competing houses, meaning that along the way several people crowned king or queen were so crowned after defeating relatives or even entirely different families (in fact perhaps the most famous line of British monarchs, the Tudors, are extinct in the male line; Edward VI, Mary I and Elizabeth I all died childless, and James VI of Scotland, Elizabeth's first cousin twice removed, ascended the throne under the House of Stuart). However, in the normal course of events, the line of succession of rule is by blood; principles of primogeniture apply more often to lines of kings than emperors. Emperors, by the nature of an empire, usually become so by conquest; you start out ruling one country, and then you invade another and replace their former system of government with one controlled by you. The line of succession of emperors can be either by blood (dynastic) or by continued conquest; the Roman Empire is a mix of succession by blood and by usurpment. The key difference is that dynastic rule is usually less important in an empire than simply whomever has the most power and influence within it as of the death or deposition of the sitting Caesar. If the previous Caesar was well-liked, then whomever he has groomed for power (whether a child or a close friend) is likely to ascend. If the previous Caesar was disliked, or didn't leave a clear line of succession, then the situation is ripe for a power grab by a previously less influential faction which then promotes its own leader into the position.

EDIT FROM COMMENT: Actually, the title of Emperor does fit with Japanese history. Prior to the 11th century, Japan was a collection of feudal states basically ruled by the landowners. The Emperor was appointed by these aristocrats to resolve disputes and provide a "unified voice" over these many feudal lands. In the early 11th century, the Kamakura shogunate was formed in the aftermath of the Genpei War, which took governmental power from the aristocrats and Emperor and placed it with the military akin to a junta. During this time, and the following Ashikaga and Tokugawa shogunates, the feudal states on the islands of Japan became unified into what we now know as a single country, and the Emperor's position evolved into more of a spiritual leader akin to the Pope. The importance of bloodline was always central (which does indicate a king), but as the Emperor became the head of the Shinto faith the bloodline came to signify the Emperor's status as a descendant of Amaterasu, and thus having divine legacy but not necessarily the mandate to govern.

In the late 1860s the Tokugawa shogunate fell and power to govern was restored to the Emperor (at the time Emperor Meiji, hence the "Meiji Restoration"). From this time until the end of WWII, Japan did indeed become a true empire, extending beyond the home islands to assert control over Manchuria, most of Southeast Asia and the Indonesian archipelago. The treaty that ended WWII allowed the Japanese people to retain their Emperor as a cultural icon, but stripped the office of all power to govern. The position and its trappings are defined in the current constitution as "a symbol of the Japanese state" akin to the British Crown, but while the Crown retains some key sovereign powers like command of the armed forces, the power to veto and to dissolve Parliament, etc, the Japanese Emperor performs mainly ceremonial and diplomatic duties and has no sovereign power whatsoever.

The transition period from one ruler to another is often referred to as a succession period.

In a period where there is a rapid succession of rulers, you are indicating that the turnover rate at the top, for whatever reason, is swift.

The means by which a succession is forced - be it by ouster (generic term for any overthrow), coup (typically via a military overthrow, short for coup d-etat), or assassination (referring to the killing of the leader) - is irrelevant to the idea of a rapid succession or a series of successions. An ouster or a coup begins at the moment the leader is no longer in charge.

When Oliver Cromwell overthrew King Charles II, for example, the ouster began the day the King abdicated. When he was executed, the regicide was complete. To claim he was assassinated would be an overreach. He was executed after a trial, not assassinated. Had he been killed in battle, it would be referred to as such and called out as such. In contrast, if the leader is murdered without due process, it is an assassination.