A face-off is an in-person confrontation, like the face-off between rival ice hockey players or a face-off between presidential candidates on a debate stage.
You can use the noun face-off whenever two people have a face-to-face showdown. You could even describe the duel between Alexander Hamilton and Aaron Burr as a face-off (a deadly one, as it turned out). Rival groups or teams confronting each other is also a face-off, like the big championship face-off at the end of basketball season. This sports context is the way the word was originally used, dating from at least 1886.