Now I know what you are talking about, otuatail!
The "dry cooking" you mentioned is what tipped me off that this wasn't some sort of stoneware - stupid me! This is probably one of the many copper colored, non-stick (the dry cook part of the advertising) pans, with a ceramic (probably the reason for the "stone" in the name) NS coating, supposedly better than the PTFE coating, which releases toxins when overheated.
You can still put oils in any of these pans, and I'm sure that they are washable! They have no copper, so you don't have to get a copper polish, as with real copper (I never do that, anyway - just let them turn brown!). I got one - a copper colored wok, sold by Ming, and it works great, though I don't use it for my high heat SF. It works great for things like cooking down Mexican sauces and moles, due to its NS coating. I also replaced several of my old teflon skillets with some ceramic NS pans, but I noticed, while shopping for them, that many said "heatproof to 450°", and one only to 400° (and no plastic on those - just the coating seemed to have limitations), so check the instructions carefully. I got some that are heatproof to 500°, which is more like it for skillets.
And they can scratch; even if the ads say metal won't hurt them, don't use it. The scratches will not be as visible as in metal, but metal will scratch it, and those almost invisible scratches will compromise the NS ability of the ceramic coating. Also don't use a cleaner that would scratch, but you really shouldn't have to, since it cleans so easily.
Have fun with your new cookware!