Empirical studies of the social lives of non-human primates, cetaceans, and other social animals have prompted scientists and philosophers to debate the question of whether morality and moral cognition exists in non-human animals. Some researchers have argued that morality does exist in several animal species, others that these species may possess various evolutionary building blocks or precursors to morality, but not quite the genuine article, while some have argued that nothing remotely resembling morality can be found in any non-human species. However, these different positions on animal morality generally appear to be motivated more by different conceptions of how the term “morality” is to be defined than by empirical disagreements about animal social behaviour and psychology. After delving deeper into the goals and methodologies of various of the protagonists, I argue that, despite appearances, there are actually two importantly distinct debates over animal morality going on, corresponding to two quite different ways of thinking about what it is to define “morality”, “moral cognition”, and associated notions. Several apparent skirmishes in the literature are thus cases of researchers simply talking past each other. I then focus on what I take to be the core debate over animal morality, which is concerned with understanding the nature and phylogenetic distribution of morality conceived as a psychological natural kind. I argue that this debate is in fact largely terminological and non-substantive. Finally, I reflect on how this core debate might best be re-framed.