Most of the time, you'll see a White Russian blended so that all the ingredients are incorporated together. It tastes like a coffee accented thin milkshake with the vodka leaning out the richness of the cream and sweetness of the Kahlua.
You can also prepare a White Russian by stirring the vodka and Kahlua briefly on the rocks and then floating the cream on top. The ingredients have a chance to stand out individually and interplay.
Unlike the Black Russian, whose origin is fairly well documented, the origin of the White Russian is unclear. In history, the term White Russian most often refers to the anti-communist forces that fought the Bolsheviks during the Russian Revolution and succeeding cival war from 1917 to the early 1920s. But it is more probably that the name just refers to the addition of cream to the recipe.
We start to see the White Russian splitting off from its cousin in the 1950s, and appearing in bar books under its present name a few years after that.