In the game, the story is more interactive. While the anime just shows the events, in the game you can directly influence the outcome of battles. For example, in the game you can choose different combat strategies against Titans.
The story in Attack on Titan Game 2 has some differences from the anime. The game might expand on certain events or characters' backstories more. It also allows you to experience the story at your own pace. In the anime, it's a more linear progression. Also, the game may introduce some unique scenarios that are not in the anime, like special Titan - hunting missions that are designed specifically for the game's gameplay mechanics.