All of the same materials are used. The real differences are in the shapes and flex patterns. The term symmetry is used extensively in any discussion of boards because of the consistency throughout. Because a snowboard is ridden with one foot forward, the turn dynamics are obviously different from a ski. Normally a ski is asymmetrical front to back and symmetrical side to side.
Most boards have symmetry just like skis.
Usually the rider will have a preference to being regular or goofy and set-up the board accordingly. They are designed for use in all snow conditions and most can even be ridden in the halfpipe very successfully. Maybe half of all boards sold in the U.S. are of this type. They tend to be more flexible with wider foot stances more centered on the board. These boards have more nose and tail area and less effective edge than the other types.