This happens to me occasionally. Probably about once every six months or so. One time, it was so incredibly intense, that I was afraid to go to sleep for a while. I woke up to a bright, sunny morning, but found I couldn’t move. I could move my eyes, but that was it. Even though I could see my room, it felt like my eyes were closed because I was trying to will them open. My arms and legs were paralyzed. I tried yelling out but couldn’t open my mouth. I made a strangled sort of sound in my throat. I tried and tried to move, and eventually I sort of kicked my legs against the bed over and over really hard – it made this loud rumbling sound and then someone out in the hallway yelled “earthquake!” plain as day. I tried screaming again, but still couldn’t get out more than a strangled whine. I don’t know how long this lasted, but it felt like an eternity. When I finally woke up for real, I actually sat bolt upright and started grasping at the wall to make sure everything was real. I was sharing a room with my sister at the time, and I asked if she heard me yelling or stamping my legs, and she looked at me really strange and said she hadn’t noticed a thing.
There is another phenomenon called hypnogogy, that can be similar. It’s probably centred in the same part of the brain. It’s basically a hallucination (either auditory, visual, or both) that happens in between sleep and waking. It happens most commonly at night while falling asleep, or in the morning during waking. You basically dream while still being somewhat aware that you are in your bed.
Edit to add: just read the Wiki link and see that the two ARE connected. 