I don't know about two prong mains plugs (we don't have them here) and I don't know much about the US system. But in the UK we have three prong plugs, with Live, Neutral and Earth. The potential between live and neutral tends to be around about zero, whereas the potential between live and earth is around 220V.

When you are dealing with an appliance with a two prong figure-of-eight plug then polarity clearly doesn't matter, as you are free to plug it in any way around, but of course those devices aren't earthed.

I am always nervous when I use US or European plugs, they feel so unsafe compared to the chunky UK ones (whether there is any actual practical difference in safety I don't know). The US ones in particular feel like the prongs are made of tin foil, compared to the UK ones.