The convergence of next-generation wireless communication technologies and modern energy infrastructure presents a promising path toward sustainable and intelligent systems. This survey explores how beyond-5G and 6G communication technologies can support the greening of Industrial Internet of Things (IIoT) systems and smart grids. It highlights the critical challenges in achieving energy efficiency, interoperability, and real-time responsiveness across different domains. The paper reviews key enablers such as LPWAN, wake-up radios, mobile edge computing, and energy harvesting techniques for green IoT, as well as optimization strategies for 5G/6G networks and data center operations. Furthermore, it examines the role of 5G in enabling reliable, ultra-low-latency data communication for advanced smart grid applications, such as distributed generation, precise load control, and intelligent feeder automation. Through a structured analysis of recent advances and open research problems, the paper aims to identify essential directions for future research and development in building energy-efficient, resilient, and scalable smart infrastructures powered by intelligent wireless networks.