Both are false.
Displacement can be zero if the body or object remains stationary, or the object travels in a circle or a curve or in a straight line forward and traces back the path to initial position.
Magnitude of the displacement is always less than the magnitude of the distance traveled by the object. Displacement can be negative or positive. Distance is always positive. So when displacements are added using the vector addition formula, the resulting displacement magnitude is always less than sum of two individual displacements.
However, total distance is always the sum of the individual distances traveled.