At most SMC's and USMA, the Corps of Cadets refers to the entire student body that participates in the 4th class system. For example, at VMI that would include virtually 100% of the students, whereas at Virginia Tech or Texas A & M, it would be a small subset of a large non-military student body. I don't believe that the Cadet Student Body of AROTC at non SMC colleges are ever referred to as a Corps of Cadets. (Please correct me if I am wrong).
At SMC's it is generally required that members of the Corps of Cadets must participate (but not necessarily contract) with a branch of ROTC. It could be AROTC, NROTC or NROTC/MO, or AFROTC. These members of the Corps of the Cadets will take a different military science curriculum based on their specific selection of ROTC.
If a cadet chooses to contract, usually a scholarship or stipend accompanies this arrangement to financially assist the cadet through part if not all four years. Once contracted, the cadet is obligated to serve active duty in that particular branch. If a cadet chooses not to contract at an SMC, there is no military obligation upon graduation.
For Army ROTC, only SMC's (and USMA) can guarantee active duty upon satisfactory graduation from the Corps of Cadets and approval of the AROTC Professor of Military Science (PMS). At other non SMC ROTC colleges, AROTC can dictate reserves or NG instead of active duty upon graduation. NROTC and AFROTC only contract active duty.
I hope this helps! I'm just a dad and there are lots of other more seasoned experts here, but no one else seems to be awake right now.
Good luck to your DS!