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.
there realy isnt any difference.... to a lay man oscillation is the movement of a pendulum.... oscillatory motion is the continuous movement back and forth about a certain fixed point....
periodic movement is however the motion involved in complete cycle of either oscillatory or rotational or circular motion.