Given scene/plot descriptions from movies or TV shows, and given a specific question about the scene, summarize the question into a title

I was watching Batman: The Dark Knight the other day and something jogged my memory. There is a scene where the Joker puts two bombs in two separate boats and gives the detonator to the boat owners. He claims that each boat can use the detonator to blow up the other boat, before the other boat does the same. Eventually, the time limit runs out and no boats explode, thus proving that Gotham is good and redeemable. Now, I'm not sure if I imagined/dreamt/read somewhere that each boat had in fact its own detonator. If they pressed the button, they would blow themselves up, not the other boat. This would be an even larger twist on the game. Is this actually real? Is this what happens in the comics or on the original Batman movie? Or did I just read this on some theory on the web?
What did the Joker's detonators actually target?