The 12x10 and 15x12 are a true 12 or 15" long and 10 or 12" wide. The other Detech coil, the 13" Ultimate, is actually a true 13" wide but only 12 & 1/2" long. Do I have that backwards? Not sure, been a while since I measured it, but I don't think so.
Just for further sizes, if not specifically coils available for certain machines, the WOT is 14.25" in size while many call it a 15" coil. The Minelab 8" Tornado coils are actually 7.25" in size. The 5" Excelerator is actualy a bit under 5" in size. The Sun Ray S/X-5 coils are actually 5.5" in actual size. The S/X-12 Sun Ray coils are actually 12.5" in true size.
Used to own the Whites "5.3 Bullseye" or whatever they call it, and was let down that it was much bigger than the name implied for a trash coil. Off hand I can't remember, but I think it's true size was like 6 & 3/4" or something like that. I thought I was getting a much smaller coil, which to me is important for a trash coil sometimes.
Always amazes me that companies don't just name coils to the true size they are. Yea, probably not very good for a catchy name to sell by, but when I'm coil shopping for either a large or small coil I want to know exact measurements for both depth potential and/or ability to separate, where even a half inch can make all the difference.