Moon and Sun halos originate when ice crystals form in the upper atmosphere. This requires temperatures below -30°F and a supersaturated atmosphere. This is usually caused by a warm front over riding cooler air and being thrust very high up. Depending on the particular combination of temperature and percent supersaturation, different type of crystals will form. In the case of a halo they are simply 6 sided columns oriented randomly. Light traversing a 120° corner preferentially is deflected at 22° thus causing the halo.
When a column falls into a slightly warmer zone it can develop a six sided plate at one end and become a "capped column" thus falling like a dart. The six sides are now oriented perpendicular to the Earth's surface and the result is a horizontal band with parhelia at the preferred 22° angle.
There are other crystals possible along with many combinations thus many different types of arcs and halos although most of these are very rare.