We consider a communication scenario in which a public-confidential message pair is transmitted over an arbitrarily varying wire tap channel (AVWC). The public message needs to be decoded by both the legitimate receiver and the eavesdropper, while the confidential message is only decoded by the legitimate receiver while keeping it secret from the eavesdropper. For this scenario, we completely characterize both the deterministic and the correlated random capacity regions. In order to establish these characterizations, we introduce an auxiliary channel that combines the concepts of compound and arbitrarily varying channels at the same time. We then use Ahlswede's robustification technique along with the method of elimination of correlation to derive the desired capacity regions from the capacity region of the introduced auxiliary channel.