AI co-writing systems challenge long held ideals about agency and ownership in the creative process, thereby hindering widespread adoption. In order to address this, we investigate conceptions of agency and ownership in AI creative co-writing. Drawing on insights from a review of commercial systems, we developed three co-writing systems with identical functionality but distinct interface metaphors: agentic, tool-like, and magical. Through interviews with professional and non-professional writers (n = 18), we explored how these metaphors influenced participants' sense of control and authorship. Our analysis resulted in a taxonomy of agency and ownership subtypes and underscore how tool-like metaphors shift writers' expected points of control while agentic metaphors foreground conceptual contributions. We argue that interface metaphors not only guide expectations of control but also frame conceptions of authorship. We conclude with recommendations for the design of AI co-writing systems, emphasizing how metaphor shapes user experience and creative practice.