What's in a Name: Principality, Tsardom, Empire
Rus and Russian principalities and grand principalities are sometimes called "duchies" and "grand duchies" by westerners, such as the Principality of Polotsk also being known as the Duchy of Polotsk or the Grand Principality of Moskva as the Grand Duchy of Moscow (or Muscovy). "Duchies" were familiar terms to western Europeans of those times but were not used by the Rus or Russians. Instead, the rulers were princes or grand princes and their realms thus principalities or grand principalities. A grand prince in theory had authority over other princes, but this varied in practice based on circumstances. During the decline of Kievan Rus, the Grand Prince of Kiev often could not command other Rus princes and occasionally was dethroned by them.
Ivan IV, Grand Prince of Moskva from age 3, proclaimed himself Tsar of All Rus at his coronation in 1547. His state thus became the Tsardom of Russia. Like the German "kaiser", "tsar" came from the Latin "Caesar", a Roman Empire title, which itself came from the name of Gaius Iulius Caesar ("Julius Caesar"). "Tsar" thus meant "emperor" and "tsardom" (tsarstvo) meant "empire". With the popular Russian idea of Moskva being the Third Roma, it at times also implied that the tsardom was the successor to the Eastern Roman Empire and thus the protector of Orthodox Christians. In the 1800s, this in part would result in Russia fighting a war against the Muslim Ottoman Empire, Catholic France, and Protestant Britain, the Crimean War.
As Russia became more involved with western Europe, countries there misunderstood "tsardom". In 1721, Pyotr the Great, who had visited western Europe, accordingly changed the name of his state to the Russian Empire (Rossiyskaya Imperiya), explicitly using "empire" in its name in a way westerners would understand, and he assumed "emperor" as his own title. ("Tsar", however, remained the popular title for the Russian emperor.) Whether westerners realized it or not, Pyotr was declaring his ambition that Russia would be at least equal to the great powers of Europe, rather than some distant, backward, oddly-named country.
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More of What's in a Name: Tsar and Czar
"Tsar" is Russian for "emperor" and ultimately derives from the Latin "Caesar", just like the German word for emperor, "Kaiser" does. Interestingly (at least to me), the Slavs/Rus apparently did not derive "tsar" from the Greek "kaisar", even though they were in contact with the Greek-speaking Eastern Roman Empire for centuries. Instead, it is believed they derived "tsar" either directly from the Latin word or indirectly via the Goths' "kaisar", which went on to become the German word "Kaiser".
But, what about "czar"? This is an alternative spelling. "Czar" seems to have come from Austria, via the Polish word "car", which the Poles pronounced "tsar" (Polish "c" is often pronounced "ts"). It is believed the Austrian who coined "czar" added the "z" as a guide to pronunciation, since in German "z" is pronounced "ts". From Austria, this spelling spread to several western European countries. Other variant spellings include "tzar" and "csar". Overall, the Russian ???? transliterates most naturally as "tsar".
More of What's in a Name: Emperor
Empires have existed for well over 4,000 years, although the term went out of official use in the second half of the 20th Century as imperialism and colonialism increasingly became condemned. (Japan officially still has an emperor, but the country changed its name from "Empire of Great Japan" (Dai Nippon Teikoku) to "State of Japan" (Nippon-koku, also Nihon-koku) when it became a constitutional monarchy after World War II.) Despite the long history of empires, the word "emperor" only came into use in its imperial sense about 2,000 years ago.
Of course, the early empires had emperors, but they were typically called "kings" (in their own languages). The emperors were more powerful than "mere" kings, and in various places in ancient times a sense of "emperor" developed. For example, the ruler of the Persian Empire was "king of kings" and "king of the world", among many other titles.
The Romans almost by accident turned the meaning of their word imperator into "emperor". Long ago, the Romans had gotten rid of their kings and became a res publica with elected government officials, assemblies of citizens, and an unelected senate that controlled things like state finances, foreign policy, and other important matters. This is called the Roman Republic, although it wasn't a republic in the modern sense. It was illegal, with penalty up to and including death, to seek kingly power over Roma, and overly-ambitious politicians could have their reputations tarnished with the suspicion that they wanted to become king. In crises, when a king-like leader was needed, the republic would appoint a short-term dictator with great but not unlimited powers.
Over time, the armies of the Roman Republic gained control of the lands around the Mediterranean Sea and nearby areas, so that the republic controlled a vast empire of other peoples. Empire made the republic increasingly unstable, as far-off governors of provinces held immense power, generals in campaigns of conquest in distant lands had little control over them, powerful individuals gained immense wealth and vied for political power, often violently. Powerful generals were both a necessity and a threat. Soldiers increasingly became more loyal to their general rather than to the republic at large, and for a general they particularly liked they would voluntarily call him "commander", imperator in Latin.
Finally, Gaius Julius Caesar with his army of loyal soldiers defeated his rivals in civil war and in 45 BC was effectively in control of Roma and its empire. Although he did not officially try to become king, he took the titles or powers of most of the top government positions and made himself dictator in perpetuity. This was too much like a king for some Romans, who assassinated Caesar in 44 BC.
The assassination sparked a new civil war, won by Caesar's adopted son "Octavian" (born Gaius Octavius, becoming the younger Gaius Julius Caesar, son of the elder Gaius Julius Caesar, when he was adopted). Octavian was now in control of Roma and its empire, but he did not overtly grab power like his adoptive father. Instead, he pretended to cede full power to the senate, which in turn over time granted him various government positions and privileges. Octavian maintained the pretense that he was just "first citizen" of the republic, first among equals. He also had the senate "grant" him the title of Augustus, the August One, and Augustus became the name most associated with him as emperor. Later emperors would adopt the names Caesar and Augustus, so that both names over time came to mean "emperor".
During his time as a general, Octavian was proclaimed "imperator" by his soldiers 21 times, something he liked to boast about not just for vanity but also to remind people he had the backing of a powerful army of loyal soldiers. While he never fully dropped the pretense of being just the first citizen, as he aged he changed his official name to the bombastic "Imperator Caesar Divi Filius Augustus" (roughly, Commander Caesar, Son of a God, the August). Divi Filius came about because Octavian had the senate proclaim the elder Gaius Julius Caesar a god, thus making him the son of a god, which of course was a powerful political statement.
Within decades, Imperator became a title only for the ruler of the Roman Empire and acquired its sense of "emperor". Troops no longer proclaimed their generals "imperator", except when the general wanted to become the emperor and was willing to start a civil war to try to seize power. Imperator migrated to other languages such as "empereur" in French, "emperor" in English, and "imperator" in Russian -- a term Pyotr the Great in 1721 brought into Russian to elevate his own status. While "tsar" did mean "emperor" in Russian, "imperator" was more prestigious (at least to Pyotr, many Russians preferred "tsar") and was also unmistakable in meaning to foreign powers.