There are a number of words that are used when describing game play. Here are a few of the common ones.
Offense/Offence: The team that has the ball
Attack: Same as Offence
Defence: The team that does not have the ball
Referee (Ref)/Umpire: The person in charge of the game (often has a whistle!)
Self-Replicating: A game in which no player is permanently out, i.e. there are ways to get back in if you are out
Self-Managing: A game that does not require a referee
It or In: A person or people who have to chase or tag other people