Are you challenging me to a duel, Captain Kirk?! - Trelane, the Retired General of Gothos TOS: "The Squire of Gothos"
A duel is a sporting event where two or more opponents get together to battle it out; the victor is usually the one who is the one that is unscathed or generally in a better position than the opponent at the end of the event.
James Kirk and Trelane, the Squire of Gothos battled each other in a duel of guns. Later, they used swords. (TOS: "The Squire of Gothos")
In the 24th century, Frenchmen, like Jean Luc Picard, used fencing to duel. He invited Guinan to participate in a duel, and she promptly defeated Picard using a fake wounded tactic. (TNG: "I Borg")