I don't know that the naming systems are consistent from one manufacturer to the next. What you have to watch for is the height of expansion cards that can be installed in the case. Most cards are full-height. If you get a very short "slim" desktop case (or a narrow tower), you will be limited to low-profile expansion cards.
This case can accept only low-profile cards:http://www.newegg.com/Product/Product.a ... 6811147098
This one accepts full-height cards:http://www.directron.com/tm210.html