Ok, here an experience I had this morning to pretty much verify they are the same thing (at least in my own experience, maybe not for you).

I woke up, barely awake, and for some reason was thinking about existence. I don't know why, I just was. I got a little spooked from my thought, and this fear sort of induced sleep paralysis very quickly. Once I realized I was in this state, I tried to roll out, but for some reason was stuck. I felt a tugging at my feet, and felt some sort of presence around me. The presence did not feel good, so I imagined a very bright and powerful ball off light on my floor illuminating the whole room. This ended up working, and I sat there and thought out loud "there is more where that came from". Anyway, so I finally roll out, and touch the ground, but I cannot move at all. I have no sight either. I feel the tugging at my feet, and feel myself start to float away. I slowly begin to make out what looks like a bunch of leaves, and soon it looked like I was looking a bunch of bushes all lined up uniformly (I was possibly looking at "the tunnel" wall here), and slowly I begin to sink. I look down and see a large town below me. A place I've never been in my life before (though a lot of non lucid dreams have this quality). I dropped from the sky and began my lucid experience. After that it was no different from a regular lucid dream.