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 object repeats a path after a regular interval of time.
All oscillatory motion are periodic but all periodic motion are not oscillatory.
Example- Consider the motion of Earth around the sun. A complete orbit takes roughly 365 days and therefore this is a periodic motion. However, cannot be said to be oscillatory. A motion of pendulum is both oscillatory as well as periodic.