The same method that creates adversarial examples to fool image-classifiers can be used to generate counterfactual explanations that explain algorithmic decisions. This observation has led researchers to consider CEs as AEs by another name. We argue that the relationship to the true label and the tolerance with respect to proximity are two properties that formally distinguish CEs and AEs. Based on these arguments, we introduce CEs, AEs, and related concepts mathematically in a common framework. Furthermore, we show connections between current (...) methods for generating CEs and AEs, and estimate that the fields will merge more and more as the number of common use-cases grows. (shrink)