Electrical load forecasting (ELF) plays a critical role in the planning and operation of modern power systems. As energy demand patterns grow more complex, deep learning (DL) techniques, and more recently, foundation models (FMs), have emerged as powerful tools for modeling temporal dynamics and integrating heterogeneous inputs. In practice, the effectiveness of these models depends not only on their architectures but also on the learning paradigms that determine how they are trained, adapted, and deployed. However, most existing surveys focus solely on network architectures, with limited attention to the underlying paradigms. To this end, we survey the DL-based ELF from perspectives of learning paradigms and FMs. It organizes the literature into four orthogonal paradigms: task-tuned offline learning, adaptive DL, collaborative DL, and general-purpose DL. This paradigm-centric perspective enables a unified understanding of how DL methods evolve to meet the challenges of ELF. It also provides a natural framework to incorporate FMs as the latest advancement in this trajectory. Finally, key challenges are provided, and research opportunities are highlighted to inform future directions.