Since I personally didn't know the answer to your question, I passed it on to Bill Emerson who must be the World's greatest authority on the subject. Here is what he says about your question:
The rifle qualification bar letters describe the course used for qualification.
Each course varied by the distances fired, the number of targets, and the number
of rounds fired. The A course was the normal infantry qualification course for
example, but if distances were limited locally due to not being to shoot at the
long distances, or if the number of rounds given to a unit for the year were
less, then shorter ranges and less rounds dictated the use of Course B, C, or D.
Some branches, such as Coast Artillery, usually fired only on the shorter ranges
since coast artillerymen would use their rifles only in a defensive manner. The
various practices leading up to the formal qualification were prescribed to
match the planned qualification course. For some firing tables, rounds had to
be fired in a prescribed time.
Training Reg 150-10, dated September 16, 1926, calls for infantry and cavalry EM
in line companies and troops in regiments fire the A Course. EM of Inf, Cav,
CA, Engineers, QMC, Ordnance, and CWS armed with rifles who do not fire "A" were
to fire any of the courses depending upon the regimental or battalion commander.
The details of who was to fire takes more than one page. The details of the 4
qualification courses take up 5 pages.