High-quality data is essential for hospitals, public health agencies, and governments to improve services, train AI models, and boost efficiency. However, real data comes with challenges: strict privacy laws, high storage costs, legal constraints, and issues like bias or incompleteness. These can reduce the reliability of AI systems. As a result, artificial datasets are gaining importance. Synthetic and augmented data offer alternatives, yet their differences and potential are not fully understood. This paper examines how both types of data are generated and used, showcasing their characteristics through practical examples. Data generation techniques—such as Gaussian Mixture Models (GMM), Generative Adversarial Networks (GANs), and Gibbs sampling—enable the creation of realistic, privacy-preserving patient records that mimic the statistical properties of real data. Data augmentation, commonly used in image and signal analysis, is increasingly applied to structured electronic health records (EHRs), laboratory values, and time-series data to enhance model robustness and generalizability. This paper explores mathematical foundations, methodological frameworks, and real-world applications of synthetic and augmented data in healthcare. We highlight how these techniques improve disease prediction, mitigate bias, and enable high-performance machine learning models, particularly in lowresource or imbalanced clinical domains. By expanding the effective size and diversity of training datasets, synthetic and augmented data serve as critical enablers for equitable, scalable, and data-driven healthcare systems.