They're called Otherkind Dice because Otherkind was the first famous game that used this resolution mechanic.

Actually, I remember an older game called Cathayan Arts of Role Play that used the same mechanic.

The dealio is:

You roll a number of dice and after you've rolled them and looked at them, you assign them to a number of categories that represent different aspects of the task.

In Otherkind it was Narration, Motion, Life, and Safety. You roll once and it resolves a whole scene and assign the values to those categories.

In C.A.R.P. it was Attack, Defense, Movement, and Special Moves. You roll once each round and assign the values to those categories.

It works for a Sands of Time game because as a player, I often had to make a choice after an unlucky jump. The blade hit the prince and knocked away half his life. Do I rewind, using up sand but get a chance to do it again without the screwup, or do I just go to the end, and start the next fight with the injury, but full sand.

But I still have another idea I'm researching and tinkering with, so I'm not sure how I'm going to do it yet.