Yes, our Swedish red is the original faluröd colour as used for centuries. the falu röd colour is identical to falurödfärg and finds its origin in the city of Falun in Dalarna Sweden. The faluröd pigment is essentially iron oxide and derives its name from its origin. Falu röd colour is essentially depending on the processing of the oxide. The color is yellow at the start as the compound Ironhydroxide is yellow. After oxidisation it becomes orange, then red as more of the substance is turned into Iron 2 oxide.
Further oxidisation turns the material into Iron 3 oxide which is black, also a colour used in Sweden.
So the colour can be determined by the oxidation and of course minor elements have their influence. Falu Röd color can be made from any Iron oxide source.
In England this type of earthpigment is also used, mainly for the landed gentry, where each squire had its own shade of red used for the manor and the cottages.
Rio Tinto is one of the biggest mining companies, named after the red colour of the river near its base mines.
Read more here: Swedish Red