Caring for Giants you go behind the area where the safari vehicles are and are generally closer to the elephants than you get on the safari. But no touching. You learn mostly about conservation efforts from cultural representatives.
Up Close With Rhinos you go back to the rhino barn and assuming the one selected wants to participate, you get to pet a rhino through the fence. You learn about their care from keepers who work with them.
No pictures are allowed backstage - though you can take pics of the elephants once you're on the viewing platform. They usually have a photographer once you finish the rhino tour to get pics with a held frame and a held sign with the name of the rhino you met. IDK if they have a photographer for Caring for Giants since you don't actually meet one.
I love them both and love that the money goes to conservation efforts for the species.