2 piece discs are better suited for performance cars which are more powerful than an everyday road car. As the name implies the disc is made from 2 pieces, namely, a bell/hat (Aluminum) and an outer ring (Cast Iron) which is then bolted together. All 2 piece discs are treated for exceptional performance.
A floating disc is bolted together using buttons, which allows the disc to “float” or have movement between the bell. This stops the disc warping under extreme temperatures due to the different expansion rate of the metals.