  The same method that creates adversarial examples (AEs) to fool
image-classifiers can be used to generate counterfactual explanations (CEs)
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.
