Artificial Intelligence (AI) and its subfields are increasingly adopted in education, yet persistent conceptual ambiguity surrounds terms such as AI, Machine Learning (ML), Deep Learning (DL), and Cognitive Computing (CC). Despite the pervasive interchangeable use of terms such as Artificial Intelligence, Machine Learning, Deep Learning, and Cognitive Computing, this practice critically obfuscates their crucial differences, inevitably leading to significant misinterpretations and hindering effective deployment strategies in educational settings. This article addresses this salient requirement by providing a stringent conceptual elucidation of these technologies, thoroughly charting their technical development, and precisely articulating their operational principles. Moreover, the present study critically examines the far-reaching implications of AI-driven advancements for pedagogical practices, assessment methodologies, curriculum design, policy development, and institutional governance. By synthesizing extant evidence and pinpointing critical nascent intelligent techniques, including recommendation engines, convolutional neural networks, cognitive tutoring systems, and knowledge-graph-based reasoning, this article furnishes educators, researchers, and policymakers with an important, structured framework to comprehend and strategically harness the transformative potential of intelligent technologies in shaping the future of education. The comprehensive understanding derived from this framework can subsequently inform the development of robust AI-driven educational tools and strategies. Such a framework is essential for navigating the complexities inherent in integrating advanced computational systems into learning environments, ensuring that these technologies are employed effectively to enhance academic outcomes and administrative efficiency.