Astral Projection is an older term for OOB or OBE, basically the same thing.
In lucid dreams there is a break in self-awareness from being awake in PMR and awake in your dream, while in AP/OBE there isn't.
You could break these terms up even more (I think Robert Bruce makes a distinction between AP and OBE) and there are exceptions but that is the general answer. Really, it's all just a a data stream like Ted said.
I agree with this. The main additional point I would add is that OOBE's often build themselves around the scene you just left in PMR. A typical scenario would be a vibration state, followed by finding yourself in a scene close to if not identical to the scene you just left.
But you mentioned ESP and remote viewing which is why I offer that difference. Since mastering OOBE often leaves you in a known condition (perceived location wise) you can plan accordingly and design experiments around that pattern.
These are all amazing human experiences we are eluding to. But you really need to explore lucid dreaming, before worrying much about OOBE or designing PSI experiments. That may be the best natural progression for you. My opinion.