The Americans had a number of 76 mm guns that fit into Sherman tanks. At first, this was the 76 mm T1 (later M1), installed in an M4A1 tank with a regular turret in 1942. This kind of installation turned out to be unacceptable, as the turret was too cramped and the gun itself needed improvements.

In 1943, an improved variant of the 76 mm M1 gun, called M1A1, was designed. The gun was changed to be better balanced, which allowed it to function better when installed in a tank. A different turret was also used, the T23 turret left over from the Medium Tank T23 project. This turret and this gun, installed into an M4 composite tank, resulted in the experimental M4E6 tank, which passed trials and was approved for service. Since the new turret didn't need a new turret ring, it was possible to produce a whole family of tanks with 76 mm guns: the M4A1(76)W, M4A2(76)W, and M4A3(76)W. The W stood for "wet ammo rack", another feature that was added to Sherman tanks around this time. The M4(76)W was scheduled for production, but never built.

The M1A1 was better than the M1, but still had room for improvement, one of which was the installation of a muzzle brake, as well as changing the rifling twist. Guns of this type were called M1A2. M1A1 guns were also modified for installation of a muzzle brake without changes to the rifling. This variant was called M1A1C. There are also versions of the gun with rifling, but without a muzzle brake, in which case a counterweight is screwed on to balance the gun and protect the thread on the barrel.

Since the M4A2(76)W was in production during this time, you can see tanks of this type with any of these guns. However, the M4A2(76)W HVSS, or M4A2E8, came out after the design of the gun was already settled, so you only see tanks of this type with the M1A2 76 mm gun.

In conclusion, an M4A2(76)W can have the same gun as an M4A2E8, but not necessarily.

Sources:

P. Samsonov The Longest Millimeter

R.P. Hunnicutt, Sherman, A History of the American Medium Tank