Question

what is the distinction between magnitude of displacement over an interval of time and the total length of path covered by a particle over the same interval

Answer 1

Displacement is the difference between the final and initial position of a point. It is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
The magnitude of displacement is the “length of the vector”.
Distance - length of path - is a scalar quantity that refers to "how much ground an object has covered" during its motion.