The programs used by the player are called "client-side programs" or "clients". This is standard computer terminology: the game server (Host) runs the game, and people use their client programs to talk to it and play.
Basically, there are two official clients available from Tim Wisseman (DOS Planets, Winplan), and a number of 3rd party clients. There's a gentlemen's agreement in the VGAP universe that all 3rd-party clients require a registered official client before they offer registered features.
3rd-party clients: