Team Chaotix joins the formation gimmick in Sonic Heroes, Sonic Team's 2003 platformer that groups characters into speed, flight, and power. The GameCube was a lead Nintendo version of that multiplatform adventure, with Team Sonic, Team Dark, and Team Rose each running the same stages for different reasons.
Swapping the leader mid-run changes whether you grind, fly, or smash a barrier. The Chaotix are the detective team, and their story is the comic one beside Shadow's heavier plot.
Formation swapping is the whole move set. The cube release sits among the lead versions, not a much later portable cut.