An LOA stands for "letter of assurance" and it means that the Academy is GUARANTEEING YOU ADMISSION as long as you complete the remaining parts of your application (like securing a nomination, getting medically qualified, etc). An LOI stands for a "letter of interest" and means that USAFA is INTERESTED in you as a candidate and is encouraging you to complete your application, However, an LOI IS NOT a guarantee of appointment like an LOA is. An LOE is what USMA calls their version of an LOI, and it stands for "Letter of Encouragement". It basically means the same thing, USMA is interested in you as a candidate, and is encouraging you to complete your application. While it is not a guarantee of appointment, candidates who receive an LOE from USMA can schedule an overnight tour.
On another note, candidates who receive an LOI can later receive an LOA. My classmate received an LOI back in November and then received an LOA from USAFA in February and all he needs is a medical waiver to fulfill the requirements of his LOA and get an appointment.
Hope this helps!