Most games that feature a health system just track a character's general well being through a scale. Some games takes the ability to simulate violence one step further, and allow for individual body parts to be specifically damaged. The consequences vary, but a typical example is a loss of movement speed if a characters legs are damaged.
Injury in games often follows different rules than health. While health is often regenerative or quickly healed through the use of various common healing items, injury is often more serious. Many games require the player to complete a separate task to heal an injury, whether it be to visit a doctor or surgeon or administer a special item to heal an injury.