If a character appears as a boss fight first and is later unlockable as a playable character, they have been Promoted to Playable. If the two characters play similarly enough to one another, the battle may serve as a Mirror Boss.
May overlap with Previous Player-Character Cameo and Rogue Protagonist if it takes place in a sequel. Even if it's not to the death, the outcome of who wins may cause the story to branch off in different paths. If the battle is fought to the death, it can become a powerful Player Punch, especially the player is forced to decide which character lives and who dies.
If the two playable characters are rivals or Arch Enemies to one another this is all but guaranteed to happen at some point. And then there are some that pit one player character against another, controlled by the player and the AI, respectively. Some feature more of them, with the player controlling each one of them in turns. Most single-player video games have a single Player Character whom the player steers throughout the adventure.