Thanks for the thread!
I posted quite some time ago, making a distinction on what the "skier" was doing, and trying to be funny, I came up with the name "mono-skier" for the snowboarder who was doing it right. Little did I know that the name had already been taken for a snowbard in which the toes were pointed in the direction of travel!
It's all the same sport really, you apply forces to the snow/ice with a tool attached to your feet that applies pressure to the snow and the reaction force accelerates you as it's pressure distribution shapes your tool which changes the forces you can apply.
I prefer to face the direction I'm going, so I think a mono ski would suit me better, but ski's suit me even better. For fore and aft balance and applying fore and aft forces, the snow-board, with a foot nearer each end would work better. At the very beginning learning phase, I suppose the board might encourage such bad behaviour as skidding instead of carving and maybe skidding along slowly helps one aquire balance skills with fewer falls, but once people get the hang of it, both can be used to carve beautiful curves down the hill.
It's all good.