Automatic transmissions do have clutch packs. I know that the auto tranny in my C280 has 25 clutch discs total.
In addition, with the new automatic transmission the brake bands are replaced by brake clutch packs. I believe this tranny consists of 3 planetary gearsets with 3 clutch packs and 3 brake packs.
1999 Dodge Ram 2500 Cummins Diesel
2002 Harley-Davidson Fatboy
Merlin Extralight w/ Campy Record