Yeah, it's Non Recumbent. It's the use of different positions in giving birth besides the traditional giving birth while lying or sitting.
Check out this video:
http://www.youtube.com/watch?v=NjtM4EtSs34
Water birth is, self explanatory, giving birth in a tub or pool of water.
Gisele Bundchen and Charlotte Church are just a few who opted for water birth.
In my case, I still prefer a vaginal delivery. But if I have to choose between a non-recumbent over water birth, I'd choose the latter!