From my experience (but also books and forum discussions) I have developed my own definitions by now, which might not be shared by everyone. It's just my own methodology now, here we go:
OBE = lucid exit into the "physical' plane (Robert Bruces RTZ) or at least an energetically similar plane with physical imprint where you can still see things that occur in the physical and get 'validations', normally for me OBE also has highly energetic / etheric symptoms such as vibrations, electric body tingling or even the kundalini snake in your torso (happened two times for me, but I hope it won't repeat), other tangible impressions are also possible such as being touched or producing telekinetic effects
AP = lucid exit via vibrational state (sleep paralysis) or other projection/phasing methods onto a different realm (astral, mental, whatever plane), can be energetic (vibrations) too
LD = just a different way of getting onto an AP / dream plane by getting lucid inside a dream with no energetic experiences and no mind split (body/mind) being felt
Dream = for me everything is mind projection, so a dream is also a projection into a dreamzone plane (author K. Leland is the one who best wrote about this)