A decanter can be thought of as a settling basin that wraps around an axis. In the settling basin, the solid particles that are heavier than the liquid move to the bottom by gravity and form a sediment at the bottom of the basin.
In the rotating drum of the centrifuge, the solid particles that are heavier than the liquid move outward by centrifugal force and form a sediment on the inner wall of the centrifuge drum.
Since forces of about 3000 g occur in a centrifuge, as opposed to 1 g in the gravitational field, the separation of the solid particles from the liquid is much faster and more efficient.