This is already pretty well explained above but yes, there is a difference between rapid cycling and mixed episodes.

Mixed episodes are when you experience some of the characteristics of mania and depression at the same time. Mine are terrible and usually include hallucinations, lots of energy, paranoia, loathing, anger, etc.

Rapid cycling is defined as 4 or more episodes a year. When I'm un-medicaed I cycle about every 5-10 minutes. It's also a horrible, terrible, terrifying experience. When you cycle that fast it's impossible to predict what's going to happen next. Most people who rapid cycle do not cycle that fast so it might not terrify them like it scares me but everyone's different.