As far as I understand:
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Astral Travel: Any conscious exploration of the Astral plane (a higher dimension).
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Astral Projection: The ability to go through the process of sleep consciously while meditating.
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Lucid Dreaming: The ability to become aware while sleeping and gain consciousness inside a dream.
Both Lucid Dreaming and Astral Projection are ways of getting to a higher state of consciousness (within the Astral plane) to then Astral Travel.
I experimented a lot with lucid dreaming and had a number of amazing out of body experiences this way. But I also experienced it with a therapist while under hypnosis (not asleep) and spontaneously while awake once.
The experiences are very subjective. There are claims that in the astral plane you can interact with other travelers, or gain information from the real world (like sending someone a message through a dream). I don’t think this has been scientifically proven. Others claim astral projection is just an intense dream about leaving your body and going to an alternate plane of reality.
It’s an incredibly complex subject. Here’s a Youtube channel/podcast called Astral Origins that goes deep into it: https://www.youtube.com/watch?v=kyEDpB-yOZE