One is a dream where you know you are dreaming (Lucid)
The other is a dream where you don’t know you are dreaming and you think you travel the astral plane
One is real and the other is not.
Both take place in the astral plane, however lucid dreams are a completely subjective creation & are subject to lower vibrational frequencies, meaning usually less lucidity, control, power etc. While astral projection operates in higher frequencies, and is a co-creation of many beings, and unlike dreams, they will not cease to exist when you’re absent.
LDs are safer & easier. AP is more difficult to achieve & there are consequences for your actions/thoughts/feelings.
Lucid dreaming is controlling your dreams.
Astral projection is your soul leaving your body.