One gets appointed to West Point.
I went to a military college and I got a “scholarship.”
Those attending with ROTC got ROTC Scholarships.
No West Pointer or West Pointer parent I have ever spoken to referred to it as a scholarship.
The process is pretty intense. You do not “forget” that stuff.
Regardless of the terms, it is a scholarship; a full ride scholarship. The appointment is the awarding of the scholarship.
I completed my degree and commission by way of the GI bill and an ROTC scholarship. I could have foregone all of that by accepting a direct Naval Academy appointment offered to me by the Marine Corps before my enlistment ended. Unfortunately, I was already engaged to be married and was not going to give up my beautiful wife of now 43 years. Accepting the appointment would have been exactly a full, room and board, all expenses paid scholarship with both scholarship and personal performance stipulations just like any other scholarship.
The appointment is the offer tendered for the full scholarship ride. There are many appointments offered that are never accepted.