There are different classes of licenses in Russia (as well as many other countries). To drive a vehicle over 3500 kg but with less than 8 seats and no trailer you need a C-class license. My father got one some time ago - it's pretty much the same process as a car license (B-class) only you take driving lessons and the test on a truck.
To drive a wheeled heavy vehicle, you'd need the same category licence as for driving a heavy truck (the legal requirements are based on weight and number of seats).
To drive a tracked vehicle, there are separate licences; but quite a few farmers have them for moving their tractors through roads.