what is difference between oscillation and periodic motion

There are two main differences between an oscillation and
a periodic motion. The first difference is that an oscillation happens in a single
direction (or in a plane) while periodic motion is generally described in 2 dimensional
(or 3 dimensional) coordinates. For example a string oscillate only in one direction,
while a car moves periodically in a closed circle. Thus one can say that an oscillation
is the projection of a 2D periodic motion an a single coordinate axis. In fact this is
why the `sin(..)` function appear in the expression of the oscillator elongation
(because it is a projection).

There is also a second
difference between an oscillation and a periodic motion. Unlike the first difference
described above which is usually overlooked this is a major difference. An
oscillation can be periodic or not. The classical example for a
non-periodic oscillation is a damped oscillation. Its amplitude decreases over time,
until the oscillation stops, thus the motion is not periodic. Only the oscillations that
happens in a nondisipative medium (a medium where oscillator energy is not lost into
heat, by friction for example) are periodic. These periodic oscillations are said to be
undamped.