my casual bag is a DGA elite shield, I usually have about 18 discs in there. I like a bigger casual bag because I like to try discs out and throw really random stuff.
I have a Lat Pro bag for tourneys. It can hold 30-40 if I stuff it with drivers. I usually pick out a solid line up for a tournament and bring plenty of backups; 5 putter, 6-8 mids, 6-8 drivers, ~4 utility discs, so about 25 discs maybe more, depends on the course.
If it's a dink and dunk I'll carry just 10 or less discs. 3 putters, 2 mids and a driver or two, and my utility discs.