There are three main kinds of trains: SV, kupe and platskart.
Platzcart class
Russian platskart is a common carriage, meaning that you share the whole carriage with other passengers, but, of course, you have your own bunk bed. A train car fits up to 54 passengers in platskart with no separate compartments/rooms.
Economy class (54 people in one car with no separate compartments/rooms)