Mafia is a game of secrets. A few players are secretly Mafia and try to wipe out the town. Everyone else is the town and tries to find and vote out the Mafia before it is too late. The app deals the roles, narrates the night and counts the votes, so nobody has to sit out as host.
Save and leave keeps the game at the start of the current night or day, so you can resume it from the setup screen. End game throws it away. Your player list stays either way.