Let's just say that I have never snowboarded before, and it showed. A completely different experience from skiing.
You do indeed rotate the board 90 degrees when snowboarding. Steering is now front to back, with speed related to shifting left over the front of the board. No idea if the board reacts to the opposite orientation, which is to say so that your right side is over the front of the board.
Anyway, I thought it was germane to my previous post.