Astral projection is not dreaming. You can Astral project while dreaming but they are not the same. This is because when asleep your 3rd eye is natural more open, meaning you are more attuned with the spiritual world. So sometimes you can astral project without knowing it when dreaming. That said, not every dream is astral projection.
You can create a personal realm on the astral plane. So you could go into while dreaming because of the reason above, but it wouldn't be only for dreams.
Think about two kinds of astral projection; conscious and unconscious. In conscious astral projection the person becomes aware of the subtle body when it is separated out of the physical body. In unconscious astral projection, the astral body separates but the person is not aware of it.
So from that, astral projection as we normally use the terms means only being conscious during an astral projection. Each time the physical body sleeps, the astral body separates but we are not always conscious of the separation.
There is a term which is called "lucid dreaming" which is also a kind of dreaming, and this is what you asked about. Lucid dreaming means that you become aware of the astral world even when your astral body has not been displaced out of the physical system. In that case your mind is totally attuned to the astral body and is not specifically aware of the physical one, only slightly aware of it.
Regarding if dreams are different to astral projections that depends on what you mean by dream.
Dreams which are merely ideas in your mind which appear to be real to you in that state is not astral projection. But you can be in an astral projection and interpret the experience as just a dream, as just your imagination at work, while in fact it is an experience in an objective astral world
It's my opinion that astral projection, dreaming and lucid dreaming are intertwined in the same locale. The difference between dreams, projection and lucid dreaming is what is at the controls (the conscious mind or the subconscious mind). Even if you get the vibrations and roll out of your physical body, you will end up "dreaming" very quickly if you don't know what you're doing. People say, "I failed because I fell into a dream." Well, no you didn't, you just gave up conscious control to the subconscious mind which makes the experience totally different!
But yet, astral projecting and just dreaming are not the same things as I said. But there is a connection between them for sure. You may want to look for definitions in google about the terms "astral projection","dreaming" and if you want also check for "lucid dreaming".