I found an interesting paragraph in the article [1] from Buzzfeed:
"But critics say [positive gestures from China towards Uighur] are overshadowed by the government’s more repressive measures, which have fueled the propaganda of a small number of extremists, including the Turkestan Islamic Party (TIP), a radical Uighur militant group, some of whose adherents are believed to have been active in Syria and Afghanistan. According to a translation by the Middle East Media Research Institute, TIP released an issue of its online magazine on Aug. 29, calling for its fighters in Syria to prepare for future battle against the Chinese state in East Turkestan, a name many Uighurs use to refer to Xinjiang.".
The last sentence there struck me as unusual given what that implies: [2]
"The medieval Persian toponym "Turkestan" and its derivatives were not used by the local population of the greater region, and China had its own name for an overlapping area since the Han Dynasty as Xiyu, with the parts controlled by China termed Xinjiang from the 18th century onward. The historical Uyghur name for the Tarim Basin is Altishahr, which means "six cities" in Uyghur.
Starting in the 20th century, Uyghur separatists and their supporters used East Turkestan (or "Uyghurstan") as an appellation for the whole of Xinjiang, or for a future independent state in present-day Xinjiang Uyghur Autonomous Region (presumably with Ürümqi as its capital). They reject the name of Xinjiang because of an allegedly Chinese perspective reflected in the name and prefer East Turkestan to emphasize connection to other westerly Turkic groups. However, even in nationalist writing, East Turkestan retained its older, more narrow geographical meaning. In China, the term has negative connotations because of its origins in European colonialism and present use by militant groups."
[1] - https://www.buzzfeednews.com/article/meghara/the-police-stat...
[2] - https://en.wikipedia.org/wiki/East_Turkestan