Cdeg is another way of saying "In degrees defined by the Celsuis scale starting from absolute zero". So it is the same as Kelvin.
degC is another way of saying "In degrees defined by the Celsius scale starting from the freezing point of pure water at sea level". As for missing zero by a about six microdegrees, it is because when units are used, the values are always converted to base units. The base unit for tempurature is Kelvin. 0 degC just happens to be a bit off from what a computer can give for that many degrees Kelvin. I am not sure why it is changing your input, however.
