A wet system injects fuel alongside the nitrous, so (in theory) you don't have to touch the fuel system. This is simple but often dodgy. It only takes a small lean out on gas to turn your pistons into swiss cheese.
A dry system, as you've probably already guessed, only injects gas. You're on your own with fuelling - either a microfueller (dodgy) or a reprogrammed standalone ECU (not dodgy).