At Busch, the safari jeep you pay for is a 'real' safari experience. You go out onto the plains, see some animals up close and feed some of them.
Rhino Rally is a thrill ride version of the Safari ride. You have a tour guide driving your jeep, start to go around the track like you would on a normal safari but then 'something goes wrong!!!' Bridge collapses, your truck floats down the river. It's pretty fun. Although it doesn't do that anymore because Cheetah Hunt spited it.
The Animal Kingdom safari is the best one. A really varied array of animals and exhibits and a cute, 'believable' storyline to supplement this if the animals aren't up to much. Good times.
All three versions are supervised, I can't see a safari attraction working properly without a ranger type person to guide you. Wouldn't feel right.