Well and in the Moat / Secret Chamber case, it only matters in the Throne Room etc. sense - nothing is keeping you honest, but if it really mattered in say a tournament then someone could come over and watch to make sure you were honest.
Wait but there's the uh Market Square case someone pointed out. Let's see I trash Cultist to Altar, I decide to resolve Market Square first, discard it and gain Gold, then resolve Cultist and draw three cards, shuffling, and draw a Market Square. Is it the same one?
Even if the rule isn't stated in a rule book, Nate over at BGG recently explained pretty well why we can
infer that you have to be allowed to reveal the same Secret Chamber twice. You actually may not want the other players to know which cards you kept and which cards you put back, which means they can't track what you're doing with the cards on your hand. They can't know whether you're now revealing the same SC again or a new one, or maybe you had two in your hand to begin with. But I guess this is what you meant by keeping you honest.
But the Market Square scenario changes this. (And I'm pretty sure I was the someone who pointed this out.
) Again we can infer that you have to be allowed to discard the same card twice. And this time there's no way around it, since you don't necessarily know yourself if it's the same one.
So my thinking is that it should ideally be the same for both cards. You can reveal the same card several times. But of course I've never actually seen the SC scenario played. I wonder if anyone has?