Dry Ice is solid carbon dioxide. It's roughly minus 100 deg F. It goes from a solid to a gas at atmospheric pressure and temperature. It's the technology that was used to clean the Statue of Liberty several years ago. I haven't looked at the commercial units but I'd guess they generate their dry ice from liquid carbon dioxide.
Soda blasting is done with sodium bicarbonate (baking soda). It s a solid that is somewhat soluble in water. I think the blasting can be done either dry or wet. It is not as soluble in water as common salt so it takes mroe than a simple rinse to get all of it off.