Short answers, pulled from the story.
A player character (PC) is a fictional character in a video game or tabletop role-playing game whose actions are controlled by a player rather than the rules of the game. The player character functions as a fictional, alternate body for the person controlling it. Characters not controlled by a player are called non-player characters, or NPCs.
An avatar is a specific type of player character whose name and image are based on a real person, such as a licensed athlete in a sports game or a historical leader in a strategy series like Sid Meier's Civilization. The avatar's real-world identity typically carries little bearing on the mechanics of the game itself.
AFGNCAAP stands for Ageless, Faceless, Gender-Neutral, Culturally Ambiguous Adventure Person, a term for a player character with no defined characteristics. It originated in the game Zork: Grand Inquisitor, where it was used satirically to refer to the player.
Character action games are a broad category of action games driven by the physical actions of player characters. The term dates back to the early 1980s, the golden age of arcade video games, when "character games" emerged to distinguish titles like Pac-Man and Donkey Kong from the space shoot 'em ups that had previously dominated arcades.
Classic examples include Pac-Man, Crono from Chrono Trigger, Link from The Legend of Zelda, Chell from Portal, and Claude from Grand Theft Auto III. These characters are generally silent protagonists with no backstory, designed so that players can project themselves into the role.
A secret or unlockable character is a playable character that becomes available only after completing the game or meeting another specific requirement. In some games, characters who appear only as bosses or enemies can become playable after certain conditions are fulfilled, or sometimes through cheating.