Both use the jaw shape to bite into the pipe. The difference is that the plumber's wrench (never heard that name, the Swedish name translates directly as "pipe

Both use the jaw shape to bite into the pipe. The difference is that the plumber's wrench (never heard that name, the Swedish name translates directly as "pipe wrench") is that you can "help" it bite initially and that means it doesn't have to have as sharp teeth. The "american" pipe wrenches always seem to severely mar what they are used on.