Mayhem: The common law crime of mayhem is defined as an act of maliciously disabling or disfiguring the victim. This is essentially the modern definition as well.
The actus reus for mayhem is that the defendant must commit an act that causes the victim an injury that either permanently disfigures him or disables him.
Chaos:
1Complete disorder and confusion.
1.1Physics The property of a complex system whose behaviour is so unpredictable as to appear random, owing to great sensitivity to small changes in conditions.
1.2 The formless matter supposed to have existed before the creation of the universe.
1.3Greek Mythology The first created being, from which came the primeval deities Gaia, Tartarus, Erebus, and Nyx.
Mayhem vs Chaos: The word mayhem usually refers to physical injury, violence, maiming etc.. Chaos usually refers to a lack of organization, structure, ... But both have a "weaker" meaning of confusion and disorder.