There is a difference between the two sides of a sheet of watercolor paper, with one side usually slightly smoother (less hairy) than the other. But I'm not sure I'd label them "right" and "wrong" because which was which would depend on what you require from your watercolor paper.
The smoother side of a paper is better if you're painting a lot of detail, while the hairier side is better if you're wanting to build up color by using use lots of glazes.
