Healthcare data rapidly increases, and patients seek customized, effective healthcare services. Big data and machine learning (ML) enabled smart healthcare systems hold revolutionary potential. Unlike previous reviews that separately address AI or big data, this work synthesizes their convergence through real-world case studies, cross-domain ML applications, and a critical discussion on ethical integration in smart diagnostics. The review focuses on the role of big data analysis and ML towards better diagnosis, improved efficiency of operations, and individualized care for patients. It explores the principal challenges of data heterogeneity, privacy, computational complexity, and advanced methods such as federated learning (FL) and edge computing. Applications in real-world settings, such as disease prediction, medical imaging, drug discovery, and remote monitoring, illustrate how ML methods, such as deep learning (DL) and natural language processing (NLP), enhance clinical decision-making. A comparison of ML models highlights their value in dealing with large and heterogeneous healthcare datasets. In addition, the use of nascent technologies such as wearables and Internet of Medical Things (IoMT) is examined for their role in supporting real-time data-driven delivery of healthcare. The paper emphasizes the pragmatic application of intelligent systems by highlighting case studies that reflect up to 95% diagnostic accuracy and cost savings. The review ends with future directions that seek to develop scalable, ethical, and interpretable AI-powered healthcare systems. It bridges the gap between ML algorithms and smart diagnostics, offering critical perspectives for clinicians, data scientists, and policymakers.