If not, then what is/are the difference(s)?
The two are not the same, though they can be caused by similar phenomena.
As the Wikipedia article you cite mentions, a coronal mass ejection is an unusual release of plasma. That plasma is released into the solar wind.
What makes a solar particle event different is that the plasma, once released, is then accelerated to greater speed/energy. The particles in an SPE can penetrate the atmosphere and cause ionization: particles in a CME are less energetic, but still sufficiently powerful to distort the magnetosphere.
I believe you will find the Wikipedia article on solar particle events to be interesting: https://en.wikipedia.org/wiki/Solar_particle_event