Wet clutch = runs in oil
Dry clutch = runs dry - many seen with vented covers like this
http://82.70.86.166/handk/images/bik.../100_0625a.jpg The original dry clutch cover as seen on the 4Valve engines plus some 2 valve ones like ST2, is a conical bolted on cover. The wet clutch has been used on modesl such as the 620 Monster and is cast as part of the casing. Don't think there are other variations, but i am no expert so willing to be corrected.
As for differences - the dry clutch is a racing design, should give more grip but will wear faster and is noisy (hence the trademark Ducati rattle) and can get very hot (i.e. in hot weather in traffic). The wet clutch is quiet, less snatchy, will not wear as fast but will (probably) not give the grip.
Wet clutches are likely to become more common on future models due to the stricter EU noise regs coming in.
There is a bit of difference between the standard clutch on the ST2 and the later ones, in that the ST4 used a lighter clutch basket. That helps in terms of letting the engine spin up faster because it has less rotating mass. As for pressure plates, I think they might be the same though, but not sure. If they are, I might have a Casoli red pressure plate and stainless srpings going spare in a few days because I am changing to a slipper clutch that doesn't use them.
Hope that helps.
[Edited on 10-9-2005 by HW]