The Smart Grid (SG) is a critical energy infrastructure that collects real-time electricity usage data to forecast future energy demands using information and communication technologies (ICT). Due to growing concerns about data security and privacy in SGs, federated learning (FL) has emerged as a promising training framework. FL offers a balance between privacy, efficiency, and accuracy in SGs by enabling collaborative model training without sharing private data from IoT devices. In this survey, we thoroughly review recent advancements in designing FL-based SG systems across three stages: generation, transmission and distribution, and consumption. Additionally, we explore potential vulnerabilities that may arise when implementing FL in these stages. Furthermore, we discuss the gap between state-of-the-art (SOTA) FL research and its practical applications in SGs, and we propose future research directions. Unlike traditional surveys addressing security issues in centralized machine learning methods for SG systems, this survey is the first to specifically examine the applications and security concerns unique to FL-based SG systems. We also introduce FedGridShield, an open-source framework featuring implementations of SOTA attack and defense methods. Our aim is to inspire further research into applications and improvements in the robustness of FL-based SG systems.