Sit-n-Go = a type of tournament without a set starting time where the player buys-in.
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Starts: when the tournament fills to capacity it starts. For that reason Sit-n-Go's are generally 10 or less players although in theory they can have any number of players.
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Buy-in: To join most Sit-n-Go's generally have a fixed buy-in. That is a fee you pay for your stack of chips, note that the number chips dont have to have a direct translation to money.
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The Starting Stack (your chips): So you can buy in for $10 an get 1500 chips or another game you might buy in for $100 and get 1000 chips.
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Prize Money: The prize money is determined by the buy-ins (and whatever the house adds) and the winner(s) are determined by which person(s) win all the chips. So your ownership of chips determines which position you take and what share of the prize money you win.
Ring Game = AKA cash game, a ongoing game table where you can sit-in with a variable amount of money and leave when it suits you
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Starts: whenever there are 2 or more players up the maximum the table sits, usually no more than 10
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Buy-in: you sit down with whatever amount you want, normaly within some higher and lower limits set by the table stakes. Whilst in most places you exchange your money for chips with fixed cash denominations, in many ad hoc/private games you can play with cash or any othe valuable items directly
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The Starting Stack (your chips): Your starting stack is the amount you sit down with, and you can exit after winning or losing money - at any time.
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Prize Money: .Because each hand is played for cash (or other valuable items) you never have to worry about your "position" as the stack in front of you is all yours to keep!
So it seems that most confusion stems from the fact that each game normally sits around 10 players and if you took a photograph of either game in play, you wouldnt be able to tell the difference.