Self bailers can be set up with a rigid metal (or on rare occasions, wood) frame that rests across the top of the raft, to which oar locks are mounted and oars attached. The other configuration is to leave the frame and oars at home and just use paddles. So the term 'paddle raft' refers to this other set up. It's just a term for a self bailer that is set up with inflated seats known as 'thwarts' for passengers to sit on. This image shows set up for both with mounted oars in the back, and in the front people using paddles.
Passengers are obligated to row, or more accurately, paddle the boat down the river. While this means work for the passengers, it makes for a very entertaining, social (and usually wet) ride! Most commercial river guides services for Colorado Whitewater Rafting run paddle boats to give the paying clients the full immersion experience.
The normal configuration for a paddle boat is to have a 'captain' sitting at the rear of the boat shouting orders to the crew and using her paddle to steer or make fine adjustments to speed and direction. The 'crew' is the rest of the passengers, with half of them paddling on one side and the other half paddling on the other making a Colorado Whitewater Rafting experience memorable.