Medical AI is evolving from static systems to adaptive models capable of continuous learning and improvement, expanding their usefulness in different patient groups and real-world settings. However, these features challenge traditional regulatory approaches originally designed for fixed-function medical devices. The United States uses a common law approach focused on the total life cycle of a product, which allows for predetermined change control mechanisms and real-world observational data to support iterative improvement. The European Union, on the other hand, adopts a precautionary approach through the AI Act and the Medical Devices Regulation, which emphasizes transparency, traceability and accountability before a product is placed on the market. Both jurisdictions share the goals of ensuring security and trusted performance, but their regulatory architectures differ due to underlying legal-philosophical traditions. Understanding these differences is critical to aligning adaptive AI lifecycle management across jurisdictions and ensuring safe innovation.