The spiral snake throws the spiral loop toward the bank and the 'snake' is executed on the downriver side. The sweep follows the spiral.
The upriver snake throws the spiral loop toward the middle of the river and is executed on the upriver side. The spiral follows the sweep.
However both casts are used with the same hand up, on the same bank, with the same wind situation as two alternatives to the single spey with a large change of direction.
Peter, I also find that the upriver snake is an "out-front snake" and it does require noticably less backcasting room than a single spey or a spiral single, or even a normal snake roll simply because the sweep is made out in front of the caster to set up for the spiral which rotates around that path.
It does take a little practice to figure out, and if the spiral is made too early or with too much gusto it's not the safest cast in the world. It's a very enjoyable cast once learned though, IMHO.
First and foremost the line must be allowed to pass well upriver before the snake is started. I also find that a small spiral and a relaxed yet energized backward sweep works best for the upriver snake with shorter lines and sink tips.