From my gut I'd say there are two - your "conscious breathing" is actually the same as your unconscious breathing process: Both are done without awareness to it

From my gut I'd say there are two - your "conscious breathing" is actually the same as your unconscious breathing process: Both are done without awareness to it and are primarily modulated via the vegetative system (O2 receptors in the carotid, hering-breuer reflex and so on). The difference being that while you're awake you can consciously affect and correct your breathing (your "meta-conscious breathing"). When you're asleep, your body has to rely on it's other unconscious mechanisms to do that.