A red team simulates adversary attacks to help defenders find effective strategies to defend their systems in a real-world operational setting. As more enterprise systems adopt AI, red-teaming will need to evolve to address the unique vulnerabilities and risks posed by AI systems. We take the position that AI systems can be more effectively red-teamed if AI red-teaming is recognized as a domain-specific evolution of cyber red-teaming. Specifically, we argue that existing Cyber Red Teams who adopt this framing will be able to better evaluate systems with AI components by recognizing that AI poses new risks, has new failure modes to exploit, and often contains unpatchable bugs that re-prioritize disclosure and mitigation strategies. Similarly, adopting a cybersecurity framing will allow existing AI Red Teams to leverage a well-tested structure to emulate realistic adversaries, promote mutual accountability with formal rules of engagement, and provide a pattern to mature the tooling necessary for repeatable, scalable engagements. In these ways, the merging of AI and Cyber Red Teams will create a robust security ecosystem and best position the community to adapt to the rapidly changing threat landscape.