I've had many experiences with sleep paralysis and that's not it at all.
I was seeing a psychiatrist at the time and he explained, in a nutshell, what was happening. Your conscious part of your brain is awake; you can reason and think as if you're awake but the rest of your "functions" are still sleeping.
For example, I felt as if the room was shaking: that was my rapid eye movement (REM sleep) that caused that illusion. The noises you hear and the shadows you see is also partly due to REM. The reason why there's fear and panic is because you are conscious and don't understand why you can't move or why you hear noises and see shadows, it is possible to control that fear once you understand why you're experiencing what you're experiencing. After a few episodes and after my psychiatrist explained to me what was going on, it was possible for me to control the fear and just go through it, eventually you fall back asleep.
But there was no "dream" or "flying away", that is probably another phenomenon not sleep paralysis...
"If ye love wealth better than liberty, the tranquility of servitude than the animated contest of freedom — go home from us in peace. We ask not your counsels or arms. Crouch down and lick the hands which feed you. May your chains sit lightly upon you, an