I have 4 of Walter A. Wood Company's wrenches. Only the one with "Wood" on both sides with holes on either side of Wood, looks like the Pitts wrench. As a matter of fact, I have them hanging one above the other because of their similarities. I think it's more likely that both companies contracted with one of Upstate New York's many foundries to make the wrenches. that being the case, the foundry may have made a generic wrench of the same type for sale to hardware distributor.
My dad used to sell foundry casting compounds in upstate New York, and I would sometimes go with him when he made calls. Allegheny Ludlum was one of them in Eastern NY State, for example, not far from Hoosick Falls where Wood was located. They were casting fire hydrants the day I visited. May they were casting wrenches earlier in the week I visited. Maybe not.