Two forms of dueling existed historically:
One, the form practiced by, for example, 19th century Americans, or Icelanders. In this view, dueling was a form of dispute settlement. Normally duelists fought to the death, or until significant injury occurred.
18th and 19th century European dueling evolved to a point where the purpose was not to kill the other duelists, but to satisfy honor - for example, a person insulted your wife, it would then be your honor duty to duel them. If you missed them with your pistol, that's okay - the important think is you risked your life in the proposition. In this one, people normally stopped as soon as someone was injured, and in some cases at the request of their seconds.
Which one do you mean?