Racing vs. Carving
There are a few differences between carving and racing:

Carvers finish their turns but racers don\'t. Carvers make complete half-circles, which would be too wide for a race course. Racers make turns that are more elongated in the direction of the fall line, and change edges before the board becomes perpendicular to the fall line. This difference is the primary reason why carving technique is different from racing technique. If you tried to carve on a PGS course, you would probably encroach on your neighbor.
Racers minimize their body movement to follow the fastest line down a course, but carvers apply exaggerated movements. Carvers often rotate their torso into the slope ahead of the long axis of the board on each turn to carve half-circles, whereas racers typically keep their torso facing a direction between the angle of their bindings and the long axis of the board to avoid over-rotation.
Carvers never skid, but the winning racer will always skid. Racers often skid or glide flat on the board, especially at the beginning of each turn.
Racers try to be as fast as possible, whereas many carving styles often result in the slowest possible speed down the fall line. Carvers can tip the board high on edge and carve tight radius turns, which generates a centripetal force that counteracts gravity and bleeds off speed. As you get better at carving, your technique will result in slower speeds, which will require you to move to steeper and steeper terrain to maintain sufficient speed to get the board to carve.
Carvers are often anti-competitive. The idea is to express yourself rather than compete.
On the other hand, there is a ski carving competition sanctioned by the FIS. Skiers turn around buoys and are rated on carving skill.

Racing is racing, and carving is carving, and never the twain shall meet.