Periodic motion is one where a body completes a certain length of its pathway with in a certain period,so from that point of view motion of the Earth round the Sun is also an example of periodic motion.
But a body is said to be in oscillation if its displacement occurs against the direction of force acting on it,which is expressed as
For,n=1 it's S.H.M
As in oscillatory motion the body completes its certain length of pathway(amplitude) with in a given period,it's periodic in nature.
But the force acting on the Earth by the Sun is not acting against its direction of displacement rather perpendicular.
Hence,an oscillatory motion completes the criteria to be a periodic motion but all periodic motions don't do the reverse.