Periodic motion is that motion which repeats itself after equal intervals of time. The interval of time is called the time period of periodic motion. Example: (i) motion of planets around the sun (ii) motion of the pendulum of a wall clock (iii) motion of the hands of a clock etc.
If a body is moving back and forth repeatedly about a mean position, it is said to possess oscillatory or vibratory motion. Example: (i) motion of the pendulum of a clock (ii) vibrations of the string of a sitar etc.
An oscillatory motion is always periodic. A periodic motion may or may not be oscillatory. For example, the motion of planets around the Sun is always periodic but not oscillatory. The motion of the pendulum of a clock is periodic as well as oscillatory. The oscillatory motion refers to the motion in which the object moves back and forth repeatedly. While periodic motion refers to the motion in which the objects repeats a path after a regular interval of time. All oscillatory motions areperiodicbut all periodic motions are not oscillatory.