Akhilesh Pillalamarri has a compact summary at The Diplomat of a messy historico-linguistic situation:
A case in point is the “Uzbek” language. This language is a modern continuation of the literary and prestige Turkic language of Central Asia, which was known as Turki, or Chagatai. Chagatai was a member of the southeastern, Karluk branch of Turkic languages, which are the original and highly Persianized Turkic languages of the settled, Turkic, oasis populations of the Fergana Valley and Xinjiang. Its ancestor was brought to the region by the first Turkic empire in Central Asia, the Karakhanids, in the 900s.
It later became a literary language after the Mongol conquests, when the Chagatai Khanate was established in Central Asia and became Turkified in language and culture by the time of Timur and his descendant Babur, the founder of the Mughal Empire. The Timurids were conquered by the Uzbeks under Muhammad Shaybani in 1500 who founded the Khanate of Bukhara. The Uzbeks were tribes from the Kipchak, a northwesterly branch of Turkic peoples. Most of the other Kipchaks, like the Kazakhs, remained nomads and herded livestock across the Eurasian steppe.
The Uzbek language was quickly lost, and Chagatai, or its colloquial dialects, were reasserted, though the ruling class continued to be descended from the Uzbek conquerors. Yet when Soviet linguists classified Central Asian languages, they declared that everyone living in Uzbekistan was “Uzbek,” a largely extinct linguistic and ethnic group, one that most people in the region were not even descended from. Furthermore, conflating two different languages together, Soviet linguistics renamed the modern Turki dialects Uzbek and the old Chagatai language “Old Uzbek.”
We’ve discussed such things here (Elif Batuman and her Uzbek teacher in Samarkand), here (Nicholas Ostler on Persian-speaking “Tajiks” supplanting Sogdians), and here (Pynchon on language reform in Central Asia), inter alia. (Thanks, Trevor!)