Initially, Rainsford thinks hunting humans is not a sport; it is murder. He says, "Thank you, I'm a hunter, not a murderer." In the end, he does kill Zaroff, but this is the end of a long journey of self defense. So, there is at least the possibility that Rainsford still separates hunting animals and killing humans. This is a possibility but a supposition. Zaroff, on the other hand, has no problem hunting humans.
Rainsford continually refuses to hunt with Zaroff. Finally, he reluctantly agrees to become the hunted only to avoid the wrath of Ivan. He is forced into the game. When Zaroff lets Rainsford go on the first day, Rainsford (presumably for the first time) knows what it's like to be hunted. Earlier, Zaroff claims he was a born hunter and has made a life of hunting. He has no remorse for what or whom he kills and probably has never felt what it is like to be hunted. But Rainsford experiences this. "Then it was that Rainsford knew the full meaning of terror." It is possibly that Rainsford will carry this new knowledge with him. In other words, Rainsford is now potentially able to sympathize and empathize with prey. This is something that Zaroff can not do, or refuses to do.
In the end, Rainsford says he is "still a beast at bay." This means that he is still being kept in the position of the prey. He turns from prey to predator in the end, but referring to himself as the "beast" implies that he also identifies with being the prey, something that Zaroff does not identify with.