T1: Originally 57 calibers long gun,[6] reduced to 52 calibers after tests in effort to improve balance.
M1: 52 calibers long version of gun adopted for use.
M1A1: M1 with longer recoil surface to allow it to be mounted on trunions placed 12 inches further forward.
M1A1C: M1A1 threaded for muzzle brake.
M1A2: M1A1C with rifling twist changed from 1:40 calibers to 1:32 calibers.
A muzzle brake was tested in January 1944, authorized in February 1944 with production starting June 1944. Not all guns received them. The threads of those without a brake were covered by a protector visible in many pictures.
From 1943, at the instigation of the head of the Armored Force General Jacob Devers, US Ordnance worked on a towed anti-tank gun based on the barrel of the M1, known as "76 mm gun T2 on carriage T3". Later interest in the project declined and the program was officially cancelled in 1945.
With the tank in the first post:
This Sherman M4A1E8 is a late war version and was an improved design featuring the 76mm M1A1 gun (71 rounds) instead of the standard 75mm and as secondary weapons the .50cal (12.7mm) M2HB machine gun and two .30cal (7.62mm) M1919A4 machine guns. The M4A1E8 tank was powered by the Continental R974 C4 9cylinder 400-460hp engine.
One of the big improvements of the tank was the HVSS suspension, which was easier in tank maintenance and allowed wider tracks, hence the "W" designation.
Source:
M1A1, M1A1C, M1A2 Gun Page | The Sherman Tank Site
Would there be an external difference between the A1 and the A2 or was it just the rifling?
Source:
M1A1, M1A1C, M1A2 Gun Page | The Sherman Tank Site