In X and Y, the Drives can be obtained by showing Genesect to a Hiker at the Fossil Lab in Ambrette Town. He says that he received the plans for the Drives from an acquaintance of his in Unova and made the Drives from them himself.
The four Drives appeared in Genesect and the Legend Awakened. Each of them was attached to a member of the Genesect Army, with the exception of the leader, the Red Genesect. While it was used with the same purpose of changing the type of Techno Blast in the movie, it was also the key item to tell each Genesect apart, with the one holding the Douse Drive having a different personality from its group.
It wasn't shown or mentioned in any point of the movie that Genesect could switch or take off the Drives.
The Shock Drive was later given to the Magician in order to reverse-engineer another set of Burn, Chill, and Douse Drives. Blake used the Burn Drive to battle Team Plasma on the Plasma Frigate, but due to it being incomplete at the time, Genesect was injured by its own attack and left exhausted after using Techno Blast on some Team Plasma Grunts. After Blake later used the Fire-type Techno Blast to save the Swords of Justice from being frozen in ice, Cobalion knocked the damaged Burn Drive off of Genesect's body, after which it exploded.
In Pokémon Adventures, the unnamed Drive attached to Genesect's back in called the Neutral Drive (Japanese: ノーマルカセットNormal Cassette).