This paper posits and tests a social cybersecurity framework to detect and characterize online trolling. Using a dataset of online trolling obtained through active learning, we empirically find that troll messages are significantly associated with more abusive language ($p<.001$), lower cognitive complexity ($p<.01$), and greater targeting of named entities ($p<.05$) and identities ($p<.05$). These effects are robust to the likelihood that these messages come from bots. We then train and evaluate TrollHunter, a theory-driven and interpretable machine learning model using the derived psycholinguistic features. TrollHunter achieves 89% accuracy and F1 score in detecting trolling messages, with an average 12.25% improvement in performance when relationally modeling conversational context. Explorations of convergent and discriminant validity reveal that our measure of trolling is more closely related to non-hateful offensive speech over hate speech, aggressive over non-aggressive speech, and that Chinese state-sponsored accounts engage in higher levels of trolling than Russian state-sponsored accounts ($p<.001$). Finally, we apply TrollHunter in a field study to compare the media targets of trolling activity compared to bots as a reference group. Bots dominate replies to exclusive right-leaning media outlets like Breitbart and Newsmax, while trolls disproportionately target outlets with mixed partisan trust like BBC and ABC. This bifurcation suggests that not only are trolls and bots different entities, but they also have different impacts in relation to driving polarization and disinformation in society. Echoing recent calls for interdisciplinary approaches that link computational models with social theory, we conclude with implications for platform regulation and policy-making to curtail the actions of diverse agents of disinformation.