Harry Potter and the Sorcerer's Stone is based the movie of same name and follows the same story line.
The Game Boy Advance game is completely different from the Game Boy Color game. The Game Boy Advance game is a top down puzzle game. The player explores Hogwarts, and must attend classes which often include a challenge of collecting a certain number of items, such as challenge stars or potion ingredients. This game features the familiar monsters from the other games in the series, such as snails and gnomes.
Source: Wikipedia, "Harry Potter and the Philosopher's Stone (video game)", available under the CC-BY-SA License.