Ive just got an E-mail from someone from the States that a CL-600 by the military and government is called a C-143A like the BAe 125,s are called C-29.
Don'T know if it,s in order for the N85.
AFAIK, the FAA is a civil organisation, operating civil aircraft. Where they do use military designations this is because the airplane in question has been modified to military standards, like C-29A N97. N85 is a CL-601-3R.