What is the difference between a Khan and a Taishi/Taisha? I'm working on a project about Kalmykia, and I always see it called as the Kalmyk Khanate, but none of the rulers are called Khan, they are always called Taishi (or Taisha depending on the text). Is the only difference that it is an Oirat word?
Technically speaking, a Khan is the titular sovereign ruler, whereas a taishi is "merely" a high ranking official. They're mutually exclusive positions, but did not always correspond to who was more powerful at a given time. In general, public opinion in Mongolia reserved the title of Khan for the descendants of Genghis Khan, while tribal leaders often took the title taishi. This was not limited to the Oirats.
In fact, it's not an Oirat word at all. Originally, taishi was an ancient Chinese government rank also known as the Grand Preceptor. It was traditionally the most senior of the Three Great Lords of State, theoretically the three highest ranking members of a Chinese government. In practice, these positions were often left vacant or used purely as honorifics because monarchs perceive them as threats to the throne.
There are two explanations for Tiashi: that it derives (a) from the Chinese Taizi, 'prince', or 'crown prince', and (b) from the Chinese taishi, 'great master', an honorific title used by northern nomadic peoples after the Liao Dynasty (see Dorontib 1979, p. 22, n. 22). The latter explanation is more convincing, given that the crown—prince system was not established in Mongolia until after the enthronement of Chinggis Qahan. Taishi eventually became taiji, a general term in Mongol for male nobles.
Onon, Urgunge, ed. The Secret History of the Mongols: The life and times of Chinggis Khan. Psychology Press, 2001.
After the nomadic Khitans established the Liao Empire in northern China, they appears to have adopted taishi as an honorific title, introducing it to the steppes. Similarly, when the Mongols conquered of China, the ensuing Yuan Empire adopted a governmental structure with significant Chinese elements which included the taishi position. For example, Toqto'a, often regarded as the last great minister of the Yuan Empire, was granted the title of taishi in 1352 as a reward for putting down a rebellion.
Mongol rule crumbled shortly after Toqto'a lost favour at court and was banished (then murdered). By 1468 the Mongols were compelled to evacuate the Central Plains. However as a polity the Yuan government continued uninterrupted for the time being, bringing the title of taishi to the Mongol steppes. For instance, the powerful tribal leader Arughtai claimed for himself the title taishi of Mongolia. However, he supported and installed Gullici, then Bunyashiri, and lastly Adai as Khan.
Arguhtai's main opponents, the western Oirats, likewise used the title taishi. Both Toghan and his son Esen, leaders of the Dzungars - at the time the ruling clan of the Four Oirats - styled themselves taishi. They installed Toghtoa Bukha, a great-great grandson of the last Northern Yuan Emperor, as their nominal Mongol Khagan, but Esen later massacred the Borjigids in a coup. Having usurped the position of Khagan, Esen named his son Öštemür taishi in his place. Esen was killed soon afterwards however, and the Khan title returned to the descendants of Toghtoa Bukha and his brothers.
The Torghuts were another one of the Four Oirats and their leaders, like Esen, were styled taishi too. After the Four Oirat alliance fell apart, their then leader Kho Orluk taishi led much the tribe west to become the Kalmyk Khanate. Thereafter their rulers were styled khans.
Dayan Khan, a great grand nephew of Toghtoa Bukha and thus a descendant of Ghenkis Khan, reunited much of Mongolia under his rule and abolished the taishi title as part of his reforms to strengthen royal authority.