The M4A3W76 as a whole was made by Detroit Tank Arsenal and Fisher Tank Arsenal. The Turret mounted was a newer T23 housing that could mount the M1A1 76mm gun.
The 76mm, the whole reason why the Sherman received the cannon was so it could knock out any German tank in one hit. The majority of opposition of the Sherman in WW2 was from weaker armored Stug and Marder tank destroyers which higher velocity guns that had better armor penetration and accuracy at a distance. However the Tiger 1 and Panther Tanks would defeat that calm with other German tanks and guns that had better optics in which most of the time Sherman Crews did not see where the fire was coming from. The M4A3W76 would be out produced by the later M4A3E8, with one inch more frontal hull armor and better offroad suspension as well as the M1A2 76mm gun with better optics and T4 HVAT ammunition.
The M4A2W76 was a M4A3 with a Diesel engine used by Canada and Soviet Union.