Whenever it comes to the decisions that a player in a game must make, certain games will reward the player by having different events happen to change the story of the game. In other games, no matter what happens, to progress the plot of a game, certain actions must be taken that you cannot avoid. These are adaptive and scripted stories respectively.
In adaptive plots, the result of a game will change based on the choices that the player made during the game. Games such as Mass Effect, Silent Hill, and almost every Telltale game have choices littered throughout the campaign of a game that will send the player down a different plot line to an end solely original.
Scripted games have other plans. These are the games that are based solely on completing tasks that are given to you. There is no room for individuality in these games and people are usually one sided based on the fact that you are following a set path that is designed for you. No doubt easier to program, these games are capitalized by the successes of Halo, Bioshock, and Megaman (featured image).
Not all games are created equal; some give you the ability to choose and some just bring you along for the adventure. Whatever your preference, the story will be worth it no matter what choices you do or do not make.