I have gone to a neurologist and, to my knowledge, they use the term "Sleep paralysis" only when you wake up and you are paralyzed (as they described, probably, on discovery channel or whatever)
I have had quite a few sleep paralysis/waking up paralyzed episodes and only a few have been scary as hell. Most have been intriguing. I've seen things flying around the room, a woman in white gliding from one side of the room to another, felt things jumping on the bed or I just lay there and enjoy the weirdness of it. The scary one was I woke up one night unable to move and was on my side and felt someone leaning over me in the pitch black. I felt a knee in my back and a hand touch my shoulder. It was scary as hell even though I knew what it was, because I was a single girl cross country truck driving and it felt like someone had sneaked into my truck and I couldn't move or see anything.