Zodiark, Jenova and Shinryu are the 3 new servers. They are not limited to PS4 players, I have been playing on Jenova on the PC since it launched during the PS4 beta phase 2.

You have to create a new character if you want to play on the new servers, they are not allowing transfers until the world economy for the servers has a time to get established and stabilized. Once the economies are stable they will open it up for transfers.