What is the difference between Coumadin and warfarin?

Semantics. All drugs have a generic name, which is assigned to the molecule that has the pharmacological effect in the body, and a brand name that is proprietary to a specific drug manufacturer. Warfarin is the generic name for the anti-coagulant that inhibits vitamin-k dependent clotting factors; "coumadin" is simply the brand name of the formulation made by a specific manufacturer.