I think that dye is a kind of stain, but that not all stains are dyes. I think TD has it right that some stains (generally called either "stains" or "gel-stains" tend not to penetrate as much as dye-stains. The other difference is that you are more likely to chatoyancy with dye-stains, and least likely with minimally penetrating stains like gel-stains. Probably a distinction without a difference if your finish is black ;-)