LOL, I really opened up a can of worms in this topic!! lol!
The "3rd" piece of a 3-piece suit is also called a vest in the US. The sleeveless sweatery garment worn over a shirt (usually by older men) is called a "sweater vest."
I think I've decided to avoid confusion and have Clark sleep shirtless. Nobody minds that, after all!
I really had no idea that the word would be that different abroad! Well, at least it makes for a more interesting conversation! Thanks FoLCs!
-Wanda