With CTW, you have a spectator select a card and then tear off the corner and hand it to the spectator as a "receipt." The spectator's card disappears from the deck and is found to be taped onto the front of a nearby window. You show that the missing corner on the taped card matches the corner (receipt) that the spectator has been holding.
Now for the second, killer phase of the trick. You fan some cards and hold it in front of the taped card. The taped card disappears from the front of the glass and appears inside of the window. The spectators can run to the other side of the window and remove the card that is stuck inside. They'll also find that the corner matches.