Both the Russian and American space programs use a refined kerosene; the Russian version is called RG-1 and is slightly denser than RP-1. RG-1 and RP-1 formulations are generally interchangeable; American rockets using Russian engines like the Atlas V are flown on RP-1 despite the engines having been developed on RG-1.
For both RG-1 and RP-1, the specifications are mainly concerned with boiling & freezing points and sulfur content. These fuels are used in regeneratively cooled engines; the fuel is passed through channels surrounding the combustion chamber to cool it. Sulfur contained in the fuel promotes carbon deposition, which impairs the cooling function, which led to rapid burn-through when common kerosene was used in such engines.
It's very common to refer to either of RP-1 or RG-1 as "kerosene" informally; without additional context, a "kerosene rocket engine" is almost certainly using RP-1 or RG-1, and will probably run on either.
I found a paper on hydrocarbon fuel optimization that notes that RG-1 has a slightly lower heat of combustion which almost exactly offsets its higher density, giving essentially the same specific impulse for the two fuels.