The characters in a game is split into two main groups, the player character and the non player characters. Many things they share but there are some special details related to each group.
Types of player characters
Has no personality or will on it's own. A empty vessel for the player to control. Usually has a name and appearance. Example: Gordon Freeman in Half Life.
A complete character made by the development team and the player has no or few options to change them. The player only control the moment-to-moment actions of the character. Example: Most games based on existing IP.
Allows the player to customize the character.
Customizable with Fixed background
The character has a name and a defined background but when the game progress the player if free on what way to take things.
Non Player Character