There are four stereotypes of approaches to role-playing games.
These are just stereotypes. Nobody actually plays 100% by any of these.
Stereotype 1: Playing The character is a virtual playing piece. A pawn. A counter. An avatar of the player. The game world is a virtual board and framing story. Some effort is made to stay within the framework of the framing story, but generally players have their characters do whatever they (the players) want. Players are generally free to use personal, out-of-game knowledge and insights in deciding their characters’ actions. Likewise, the challenges which the GM presents may not be completely natural outside the context of the game.
Stereotype 2: Rule/roll playing The player builds the character. Since the player cannot know what the character knows and cannot act as the character would act—in play, the rules and mechanics determine what happens.
Stereotype 3: Role playing This is a mix of method acting and improvisational theatre. The player authors the character, but in play the player simply has the character act as that character’s goals, motivations, flaws, etc. dictate.
Stereotype 4: Story telling The players and the GM work together to tell a collaborative story. Decisions are made based on what makes the most interesting story.