Definition of double chance
By "double down" we are necessarily talking about a type of poker tournament. The double down tournament allows the player who is eliminated early, to buy back in for the original buy-in price. Let's look at an example. You enter a €100 + €10 Double Chance tournament. The €10+ is the commission you pay to the cardroom. Let's say that for this amount, you get 1500 chips. After 30 minutes of play, you lose everything on a heartbreaking hand. You have the option (or not) to take another 1500 chips for 100 Euros (this time, chances are you won't be charged the 10 Euros commission).
Rebuy and Double Chance Tournament
The distinction between a rebuy and a double chance tournament is that the double chance tournament allows you to make a single rebuy. Often, rebuy tournaments allow you to make multiple rebuys, which is not the case with the double chance. It is also important to note that there is a limited amount of time during which you can rebuy chips. For example, depending on the tournament, you may be told that you can only pay out your second bankroll for the first 120 minutes, until the second break.