Question

difference between oscillatory and vibratory motion.

Answer 1

Oscillation is any quantity varying in a regular pattern. It can be the position of a material object, or it can be something non-tangible like electric or magnetic field or it can be entirely abstract.

Vibration is small motions of all or part of a material object.

So the overlap is when the position of all or part of a material object is moving in a periodic pattern. 

Answer 2

oscillatory motion means tro and fro movement of body about its mean position.
it can be defined as distance covered by movement about its equilibrium position.
where as vibratory motion can be in all direction.
vibratory motion is the physical change brought about due to movement of body
example for oscillatory motion : movement if swing.
movement of simple pendulum.
example for vibratory motion:
movement of strings of guitar , violin. etc