transbrake, aka stall converter, means you can sit there and give the car some revs in drive without taking off, then pressing a button (I believe some can be activated with the brakes too) and the car gets a really hard launch, kinda like dropping the clutch in a manual.
Manual shifting auto is kinda like a tiptronic, has the auto box and shifter, but with parts from a manual box in it. For all those people who want to drive something like a manual, but can't cope with a clutch ;p
I've yet to drive a tiptronic, my calais is an auto, but so's most around, and the Jatco is reasonably tough.