Hello.
Yes, Russian army uses bulletproof vests. As far as i remember types Ж-85 and Ж-86 are the most widespread. They appeared in late 80's and have been modernized. Also, modernized version of 6Б2 (which is quite old) is quite popular. This is what you can find in any military base storehouse. Professional soldiers are also given these types, but most often they prefer to buy other types for their own money. I personally know a guy who somehow managed to find US-made Modular Tactical Vest, but it was of sand colour, so he had to paint it into green. :mrgreen:
Stealthy!
In Ossetia and Abkhazia you most probably saw other types, like Voin, Vityaz' or Vyzov - there were not so many conscripts in Georgian campaign, and almost no one of them took part in battles.