The local Ford rebuilder, shop was about 5 miles away. According to a machinist who worked there, engines were rebuilt with whatever blocks were available. So if a person needed an engine for a 1963, a 390 block was selected ( any year available) , pistons, and rods, and a camshaft similar to the stock specs. IF a shortblock, that was what you got, if complete with cylinder heads, any pair of 8 bolt exhaust, cylinder heads available, were used.
So even if the tag reads C3... , the block could be whatever 390 block that was available for rebuild at that time. The machinist said they were not worried about numbers matching.