Question

A particle moves to and fro about a point. This type of motion is called motion.

Answer 1

When a particle moves to and fro about a fixed point, it is said to be in oscillatory motion. Example - a simple pendulum.

On the other hand, a periodic motion is the type of motion in which a body repeats its motion after every fixed intervals of time.

Oscillatory motion is periodic, but not every periodic motion is oscillatory motion.