While both beef barbacoa and shredded beef involve cooking the beef until tender and shredding it, beef barbacoa typically implies a specific method of cooking with particular seasonings and flavors, such as the ones used in this recipe, including diced green chilies, chipotles in adobo, ground cumin, and dried oregano. These ingredients impart a rich and complex flavor profile to the dish. Shredded beef, on the other hand, is a more general term for the texture and preparation of the meat, often slow cooked until tender and then shredded or pulled apart.