What is the difference between a round-bottom wok and flat-bottom wok?

All the answers above are correct in the western world but in Asia, round bottom woks are used on stoves that have a flat, cast iron surfaces with a large hole in it where the wok sits in it an inch or so. Underneath is a naked wood or coal fire. Usually round bottom woks don't sit safely on western gas stoves as they fall to the side but as you tend to hold them anyway and cook fast. I use a round one on my normal gas stove here in England simply because it makes everything 'feel' authentic and is part of the fun.