Periodic motion is any motion that repeats itself (same position and velocity).
An oscillation is a special case of periodic motion though a central point, typically an equilibrium location (zero net force location).
Simple harmonic motion (SHM) is a special case of an oscillation where the net force is proportional to displacement and the position as a function of time is a sine or cosine function.
A mass bouncing up and down while attached to a vertical spring is an example of...
A) periodic motion that is not an oscillation
B) an oscillation that is not simple harmonic motion