A ring game is just a cash game, not a tournament. So it is kind of the opposite of a MTT, which would be a Multi-Table Tournament. In a ring game you are able to win or lose as much money you have on the table, whereas with a tournament, you can only lose up to the buy-in amount.
Hope that helps.
This is right on. Only I would add the point that you can pick up your chips at anytime and walk away. These are just your standard cash games, 6-max (no more than 6 players) or full ring (usually 9-10 players).