The rapid evolution toward 6G and beyond communication systems is accelerating the convergence of digital twins and world models at the network edge. Traditional digital twins provide high-fidelity representations of physical systems and support monitoring, analysis, and offline optimization. However, in highly dynamic edge environments, they face limitations in autonomy, adaptability, and scalability. This paper presents a systematic survey of the transition from digital twins to world models and discusses its role in enabling edge general intelligence (EGI). First, the paper clarifies the conceptual differences between digital twins and world models and highlights the shift from physics-based, centralized, and system-centric replicas to data-driven, decentralized, and agent-centric internal models. This discussion helps readers gain a clear understanding of how this transition enables more adaptive, autonomous, and resource-efficient intelligence at the network edge. The paper reviews the design principles, architectures, and key components of world models, including perception, latent state representation, dynamics learning, imagination-based planning, and memory. In addition, it examines the integration of world models and digital twins in wireless EGI systems and surveys emerging applications in integrated sensing and communications, semantic communication, air-ground networks, and low-altitude wireless networks. Finally, this survey provides a systematic roadmap and practical insights for designing world-model-driven edge intelligence systems in wireless and edge computing environments. It also outlines key research challenges and future directions toward scalable, reliable, and interoperable world models for edge-native agentic AI.