Weldwood is (or at least was) a urea-formaldehyde resin which, when set, formed a plastic. Barge cement, on the other hand, is a rubber-based contact cement similar to Goo.
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"Not only is it not right, it's not even wrong!"
From Wolfgang Pauli, perpetrator of the Pauli Exclusion Principle<

Well... not really. Weldwood is a trade name for wood products that were at one time owned by U.S. Plywood, now a DAP product. They were more that just an adhesive company they had their fingers in many wood working products as well as plywood and paneling. 

 

Greg Martin