I experience lucid dreaming all the time. I've trained myself to enter that state.
Sleep paralysis is a completely different phenomenon. It's happened to me multiple times. When it happened, I was completely awake with full awareness of my surroundings. I just couldn't move my body or speak. Eventually, after several minutes of trying to fight through it, I was able to pull myself out of the paralytic state to sit up and move again. At no point did I go back "to sleep".
It is quite real. Not a dream.