The local Peer experiences the Game as a regular Player, in realtime, with the other remote Players. Most Games can handle a few dozen Players simultaneously. All the Peers in the Session are regular Player Peers.
The local Peer experiences the Game as a Spectator. It can see what regular remote Player Peers are doing, albeit with a few seconds delay. There can be hundreds or thousands of Spectators viewing the Game. All the Peers in the Session, except the local one, are regular Player Peers. The local Peer doesn't have detailed information about the other many Interactors or Spectators that might be experiencing the Game too.
The local Peer experiences the Game as an Interactor. It can see what regular remote Player Peers are doing, albeit with a few seconds delay and it can interact and affect the game through the Election system. There can be hundreds or thousands of Interactor Peers affecting the course of the Game. All the Peers in the Session, except the local one, are regular Player Peers. The local Peer doesn't have detailed information about the other many Interactors or Spectators that might be experiencing the Game too.