A key goal of social neuroscience is to understand the inter-brain neural relationship-the relationship between the neural activity of socially interacting individuals. Decades of research investigating this relationship have focused on the similarity in neural activity across brains. Here, we instead asked how neural activity differs between brains, and how that difference evolves alongside activity patterns shared between brains. Applying this framework to bats engaged in spontaneous social interactions revealed two complementary phenomena characterizing the inter-brain neural relationship: fast fluctuations of activity difference across brains unfolding in parallel with slow activity covariation across brains. A model reproduced these observations and generated multiple predictions that we confirmed using experimental data involving pairs of bats and a larger social group of bats. The model suggests that a simple computational mechanism involving positive and negative feedback could explain diverse experimental observations regarding the inter-brain neural relationship.