A Slim Set uses flatter cases, making a smaller package. From the product description, it also looks like the Slim Set versions do not include the extras (making-ofs, commentaries, subtitles, etc.) that the "regular" versions have, which is probably why they are so much cheaper.
I ordered the slim set, and it came in a set of three thin plastic cases. However, a while back, I got seasons 5-7 at walmart and they are really slim--the size of one normal dvd. I don't understand why this is called slim or where I can get the one slim set. Can someone help me, or is this discussion too old?