When you copied the 'game' onto the SD card, you actually only saved the save file onto the card, not the whole game. Unfortunately, you'll need to buy a separate disk if you want a second copy of a game.
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Without being too presumptuous: That sounds like piracy, and you won't get any help with that here.
No, Wii consoles have an SD slot, but I think the card only saves game details - high scores etc - rather than full games.
It's how you get pirated games onto the console - by hacking the system to boot images from the sd card.