Both waisted pellets and bullets spin when shot out of an air gun,
The difference is that the former is inherently stable due to two factors;
a)the pellet is usually nose-heavy
b)the tail is flared and the resultant drag at the rear stabilizes it to keep it flying nose first.The shuttlecock shape is perfect for dynamic balance. In fact the squash shuttlecock always rights itself and travels nose first when hit by the racquet.

The bullet has to rely just on spin to keep it stable in flight. Most air guns can not provide that kind of velocity to give enough spin to stabilize the bullet all the way to the target, resulting in open groups.