In Soviet Russia (… and present-day Russia), the police was called and continues to be called the militsiya (милиция) from the word militia. Wikipedia article!
However, the word for police still exists (полиция). The use is similar to the use of the terms astronaut and cosmonaut. They mean the same thing, but refer to authorities from a different part of the world.
I am not sure I understand. Are you saying that полиция is used in Russia to refer to police in other countries, but not those in Russia itself, or are the милиция and the полиция two distinct types of law enforcement agency within Russia, like the police and the gendarmes in France, or the city police and the sheriffs (and marshalls, and FBI, and…) in America?