You are seeing the difference between passive and active range of motion (ROM). Passive motion is the true physical amount of motion in the neck joints or spine. Full passive motion is available when you're asleep, relaxed, or under anesthesia.
Active ROM describes movement under your own power. This is how far you can turn side to side or up and down on your own. There are many factors that can decrease your active motion. The first is muscle tension or spasm. The second most common reason patients with whiplash can't turn fully is the fear of pain or reinjury. Dizziness can also stop neck motion.
Sometimes something as simple as eye movement or breathing can make a difference in active cervical ROM. When you turn your face to one side and reach the end of motion, try two things. First turn your eyes as far to that side as possible. See if you can turn your head just a little further. Now take a deep breath. As you exhale try to turn your head a little more.
You can repeat this exercise or return your face to the midline if you're uncomfortable. Try doing this once or twice a day for a few days. If you have increased pain or dizziness, see a doctor or physical therapist. You may need a more specific treatment or exercise program.