Most Russian watches use mechanical movements. Vostok and Poljot movements are the most common, however some higher-end Russian watches are now using Swiss ETA movements. Some low-end models are using Chinese movements.
If you are curious what these movements look like, check out this page at the PMaier Russian Watches Shop (based in Germany):
www.vostok-watches.com/movements-russian-watches.html
It gives pictures and data for mechanical movements by Vostok, Poljot, Molnija and ETA. The chart also lists watches that use each movement.
It's a good resource.