Interesting question. The word mayhem usually refers to physical injury, violence, maiming etc.. Chaos usually refers to a lack of organization, structure, like with government. But both have a "weaker" meaning of confusion and disorder. Don't pay too much attention to the weaker meaning unless you want to. Best, Nick

He was arrested for causing mayhem in the bar after getting drunk. The parking lot was complete chaos after the concert, nobody knew which way to go.