This Essay argues that understanding the relationship between privacy and generative AI requires splitting systems apart to distinguish between both different types of AI tools and different ways that human beings interact with these systems over time. Focusing on generative AI systems, this Essay first contends that this technology is exposing underlying weak spots in our social, technological, and legal understandings of privacy, and then offers an analytic framework, distinguishing between privacy challenges in, out, and through generative AI systems.