What is the difference between lucid dreaming and astral projection?
Lucid dreaming is the ability to become consciously aware of a dream while in it. It has nothing to do with control on at it's core. A lot of people say it's a dream you can control, because once you become lucid, you can actively interact and manipulate the dream world. It is simply a dream in which you know you're dreaming.
Astral projection is a form of an out-of-body-experience. Imagine your consciousness being separated from your physical body and entering your "astral body" (a form of being that is not limited by our know laws of the universe). When your consciousness is in the "astral body" it can freely explore various "realms" (often described as the astral plane.) Different cultures have different views on what the "astral plane" actually is.
While there is often connections and overlapping accounts between lucid dreaming and astral projection, they are two separate experiences. You don't need to astral project in order to have a lucid dream and vice versa.
It is also important to note that lucid dreaming has been scientifically proven (It's also been around for 1000s of years). While there are many historic accounts of astral projection (also an ancient spiritual practice), there is no scientific evidence that it is actually something we can experience it.