So what's the greek word for a vision of something real, yet of supernatural origin?
A good question that will take a bit of research. Off the top of my head I'm thinking of the miracle of the fishes and loaves. It's never referred to as a "vision" (horama), but clearly it was supernatural and happened in reality. I'll research possibly tonight or tomorrow, but I've got to be leaving for a few hours very soon.
Looking at some scripture there are many miracles that Jesus performed in our reality and they are of course never described as "visions".
Another supernatural event just came to mind:
Mar 1:10 And straightway coming up out of the water, he saw the heavens opened, and the Spirit like a dove descending upon him:
Mar 1:11 And there came a voice from heaven, saying, Thou art my beloved Son, in whom I am well pleased.
This is something supernatural that was viewed, yet it wasn't a vision.