A rapid cycle is that you are still only one mood at one time, it just might change very quickly. A mixed state you have symptoms of both at the same time. I have both.

The way it works for me when I'm mixed is that I have racing thoughts, pressured speach, and I feel hyper. Yet I also feel worthless, irritable, can cry at the drop of a hat. It bascially feels like my bones are trying to claw their way out of my skin I'm so aggitated. I usually am worst at reading at these times, and things make little sense to me when I do read. I want to get up and race around yet have 0 energy, and I want to be doing something constantly, but everything is boring. I have horrible anhedonia (lack of joy or interest) at these times, and everything I do frustrates me but I also get extremely bored. And I am like a powder keg in that any small thing can send me into what I call an "episode" which is where I basically have an explosion of emotions (crying, yelling, anger, and possible SI at that point.) Mixed states tend to be very dangerous in that they do push toward the more dangerous aspects like SI or suicidal thought (although I don't have many suicidal thoughts anymore, which is a blessing.)

This is just my experience with my own mixed states.