Lucid Dream: We all dream, nightly, all. We may recall or not our dreams, but we already have them. A lucid dream is a dream where we are aware we are dreaming while we are dreaming. We have this realization when we notice that we are in the dream world and we are in our dream body. We can do whatever we want, as there is no repercussions or karma here. You can also use lucid dreaming to empower a specific skill of yours or try something that you are unsure about trying in waking life. In fact, some surgeons, athletes, performers, etc., use lucid dreaming to "perform in the dream first" to "practice" and then, do it in waking life. You may have or not have control of your dream body; this is up to your skill. You will fill thrilled and excited during a lucid dream, feelings of freedom and excitement (too much will wake you up) will be present, and you will have lots of fun. I actually do have a course about this at Udemy :)
Astral Projection. We also experience Astral Projections during our slumber. More during the earlier stages of deep sleep, our soul "leaves" the physical body, always connected to it through an indestructible silver cord. Most (it can be an entire lifetime for some) will not recall anything at all from their astral projections. However, they still happen. I am sure that sometimes you had an abrupt awakening where you hear a very loud (BAM!), and it seems that you hit the bed, at high speed from a very long distance. Your heart is pounding hard, and you felt like you were falling. Unless you recall a non-lucid nightmare, most likely this is because you had a violent return to your physical body while you were in your Astral Form. I want to share from here, that this is a mechanism of self-defense that we have for Astral Projection to be safe. We cannot get lost in the Astral Plane, and we cannot die either, even if you wanted, you can't. The silver cord will immediately pull the Astral Body to your Physical Body. It will happen if someone or something touches the silver cord, whether it is the astral plane or the physical body gets physically or astrally touched. We can't stop this, and this will happen whether we are conscious during our astral travel or not.
After sharing a little about both, you might know some differences, but here are more:
Lucid Dreaming happens in our mind and the "Dream Plane" and thus, there is no karma and repercussions if you "do bad." Astral Projection happens at the Astral Plane where we navigate with our Astral Body. The Astral Plane (especially the lower astral) is very close and equal to Earth. While your "dream room" will change in many dreams, when you Astral Project you are going to see everything the same way. Time is not linear time in the Astral Plane (and it is entirely erratic in the dream plane.) So in some cases, there might be timeline anomalies (I love this word when talking of the space-time continuum.) You might see something from an older or further timeline (such an old lamp you had, or a table that you do not recognize, but love and eventually buy!) This is the real thing as you will be able to interact (to some degree) with the physical world. Such as reading something or seeing something, and then, upon ending your astral journey, being able to check against waking life that you were right accurately. Harmful intentions in this plane could either become karmic or just provide an erratic feedback (seeing something that is not real, for example, sort of misleading.) The level of bliss during astral projection is massive and much more potent than any positive feelings from a lucid dream. The afterglow from an Astral Journey is much more powerful and long-lasting than one from a lucid dream.
I want to comment on this point, as it something that I have noticed through many of my journeys. If you have some degree of worry (I wish this will last more, I want to do this, I want to do that, what if I do this), it means you are in a lucid dream. We can take goals to our lucid dreams, and during our lucid dream, we will recall our waking life during the very dream, and we will be able to reason. During a lucid dream, you may "worry" about waking up, or you want to get a particular goal done. It is all fantastic, but belonging to the dream world. Now, on the other hand, when you can exit your physical body you cease to perceive linear time. With this alone, when you are out of your body, you will not be thinking if you are going to return sooner or you will not have the needs (at an ego level like in dreams) to complete a specific task. You may have an ego-less desire to do so. When you think if you will return to your body, you will find yourself within it already, but not during the projection. During projection, nothing matters, you are in absolute bliss, and you will perceive only the here and now. Your joy will raise beyond measure. It feels like pure consciousness and many times like you do not even have a body (vs. a dream where you are aware of your body, whether it is as is or differs.)
If you are in a lucid dream and you think of your body, nothing happens, probably, or you could spawn a clone. If you think of your body during astral travel, you will find yourself within it immediately.