The implementation of machine learning and artificial intelligence as contemporary technologies and their integration in healthcare systems raises questions concerning data privacy and protection, which are regulated by the General Data Protection Regulation in the European Union and the Health Insurance Portability and Accountability Act in the United States. This paper is focused on examination of these two regulatory frameworks and their impact on the legal and technical incorporation in healthcare settings. It discusses the necessary measures for ensuring data privacy, security, and ethical standards that healthcare institutions must consider in the implementation of advanced methods and technologies for improving patient care, diagnostics, and operational efficiency. The comparative analysis highlights significant similarities and differences between these two regulations, particularly in the areas such as encryption, access management, and international data transfers. Additionally, the study underscores the need for new technologies to adhere to ethical principles, promoting transparency, fairness, and accountability in their decision-making processes. Finally, the paper addresses potential future paths for aligning technological advancements with evolving regulatory requirements, aiming to support compliance while fostering the safe and efficient use of modern technologies in healthcare.