Do I spread thinset on the tile, the floor, or both?
Either or both. Usually floors are gridded out, and then the thinset is spread on the floor. It’s a lot easier and quicker. However, for those who would rather backbutter the tile, that’s fine, too, as long as you flat trowel thinset onto the floor to “burn” it into the floor. In other words, you want to make sure you get a good bond by pushing the thinset into the “grain” of the floor, be it concrete, backerboard, or plywood.