A motion repeats itself after an equal interval of time. For example, uniform circular motion.
There is no equilibrium position.
There is no restoring force.
There is no stable equilibrium position.
Oscillation Motion
To and fro motion of a particle about a mean position is called an oscillatory motion in which a particle moves on either side of equilibrium (or) mean position is an oscillatory motion.
It is a kind of periodic motion bounded between two extreme points. For example, Oscillation of Simple Pendulum, Spring-Mass System.
The object will keep on moving between two extreme points about a fixed point is called mean position (or) equilibrium position along any path. (the path is not a constraint).
There will be a restoring force directed towards equilibrium position (or) mean position.
In an oscillatory motion, the net force on the particle is zero at the mean position.
The mean position is a stable equilibrium position.
Simple Harmonic Motion or SHM
It is a special case of oscillation along with straight line between the two extreme points (the path of SHM is a constraint).
Path of the object needs to be a straight line.
There will be a restoring force directed towards equilibrium position (or) mean position.
Mean position in Simple harmonic motion is a stable equilibrium.