Öne thing would be different, the Soviets would have moved Russians into Mongolia.
It is more complicated than that. Soviets
would have move people into Mongolia, as the region was (and remains) seriously underpopulated, both in terms of headcount and (even more) in terms of availability of workforce for industry. Even IOTL a lot of mining in Mongolia had been done by Soviet-Mongolian "Joint ventures", using imported Soviet workforce. Would USSR annex Mongolia, this process would be increased ten-fold. People would be recruited from all corners of USSR to go build mines and plants in Mongolia. However, ethnic Russians would dominate migration for following reasons:
1. Russians are by far biggest ethnic group of USSR
2. European Russia is one of few areas in the country seriously suffering agrarian overpopulation, and a lot of immigration waves had been fueled by peasants from this area.
3. Other Slavic ethnic groups tend to identify themselves with Russians, when they're minority within non-slavic region. For example, all the Belarussian migrants in Eastern Prussia and Karelia started to identify themselves with Russians within couple of decades IOTL.
It is also worth noting that Mongols would not give a damn to distinguish Russian from Ukrainian from Belarussian from Armenian from Georgian from Azeri, especially taking into account that they would all speak Russian. For Mongols they all would be "Russian migrants" (this is what happened in Baltics IOTL).
This course of events would somewhat harm development of Mongolian ruling elite. IOTL Mongols had to have local candidate of every position within government, and this caused huge growth of educated class (kinda like "affirmative actions" effect). ITTL there would be a choice between an urbanist migrant and a pasturalist Mongol to fill a position, so Mongols, even without any official anti-Mongol policy, would lose a lot of opportunities.