Within Buddhist thought, this is a distinction without practical difference. Remember that Buddhism states that everything is continually becoming (I think this is correct) and thus existence is synonymous with becoming. Therefore, to cease becoming is to cease existing, which is the goal of all thoughts and deeds of the eightfold- path, as is taught in the ancient Buddhist texts. That recent Western Buddhism has watered down these concepts to make the ideology more palatable to Western tastes does not make it not exist within the original canon.