From Bulbapedia, the community-driven Pokémon encyclopedia.
about to throw a Snag Ball
A Snag Ball is a type of modified Poké Ball seen in both Pokémon Colosseum and Pokémon XD: Gale of Darkness. It is created by using a Snag Machine, and it is the only type of Poké Ball which can Snag an already caught Pokémon in the games.
It was initially developed by Cipher so Team Snagem could steal Pokémon from their Trainers and give them to Cipher, who would then change them into Shadow Pokémon. However, in both Pokémon Colosseum and Pokémon XD: Gale of Darkness, they are used by the main characters for the opposite purpose: to steal back the Shadow Pokémon from Cipher and purify them into normal Pokémon. In Pokémon Colosseum, they are the only type of Poké Ball the main character uses, since there are no wild Pokémon to be found in Orre. In Pokémon XD: Gale of Darkness, Poké Spots are introduced and normal Poké Balls can be used, but snagging Shadow Pokémon with Snag Balls is still the primary method of catching Pokémon.
A Pokémon is being caught in a Snag Ball
When thrown, a Snag Ball is only visually different from a normal Poké Ball by five streaks of white which appear around it and close on the Pokémon being snagged as the Ball does. This effect looks like a hand grabbing the Pokémon. When a Pokémon has been caught with a Snag Ball, it does not say in the Pokémon's profile that it is contained in a Snag Ball. Instead, it says in the profile that its Ball is the type of Poké Ball which was initially converted into a Snag Ball. Presumably, this means that once the Pokémon is snagged, the Poké Ball reverts to its normal form.
The Poké Balls used by Mewtwo in the first movie resemble Snag Balls in that they can capture a Pokémon that already has a Trainer, although Mewtwo's Poké Balls could catch regular Poké Balls too, hinting at the Mewtwo Balls simply being storage devices.