Automated Guided Vehicles (AGVs) and Autonomous Mobile Robots (AMRs) are among the key enabling technologies driving intelligent logistics and industrial automation. Despite their widespread adoption and rapid technological evolution, the literature often addresses AGV and AMR systems in a fragmented manner, lacking a structured methodological perspective that highlights their architectural foundations, levels of autonomy, and technological maturity. This paper presents a methodological survey of AGV and AMR technologies, focusing on system-level architectures and core functional components rather than isolated algorithms. The survey systematically analyzes key technological dimensions, including sensing and perception, localization and positioning strategies, navigation and path-planning approaches, communication infrastructures, and multi-robot coordination mechanisms. A clear distinction is drawn between classical AGV systems, which rely on fixed infrastructure and predefined routes, and AMR systems, which exhibit adaptive, perception-driven, and self-configuring behaviors enabled by artificial intelligence techniques. Rather than proposing new algorithms, this paper organizes existing approaches into a coherent framework that highlights technological transitions from infrastructure-dependent guidance to autonomous, data-driven navigation. Recent trends such as cloud–edge integration, learning-based navigation, scalable fleet management architectures, and cooperative multi-robot systems are reviewed and discussed from a methodological standpoint, emphasizing their role in increasing flexibility, robustness, and operational efficiency in industrial and logistics environments. The survey also addresses cross-cutting challenges, including system transparency, safety and certification, interoperability, and sustainability. Finally, the paper outlines research directions aligned with the principles of Industry 5.0, highlighting the need for human-centered, resilient, and scalable AMR and AGV systems capable of safe and explainable operation in complex industrial contexts.