Job shop scheduling holds significant importance due to its relevance and impact on various industrial and manufacturing processes. It involves dynamically assigning and sequencing jobs to machines in a flexible production environment, where job characteristics, machine availability, and other factors might change over time. Genetic programming and reinforcement learning have emerged as powerful approaches to automatically learn high-quality scheduling heuristics or directly optimise sequences of specific job-machine pairs to generate efficient schedules in manufacturing. Existing surveys on job shop scheduling typically provide overviews from a singular perspective, focusing solely on genetic programming or reinforcement learning, but overlook the hybridisation and comparison of both approaches. This survey aims to bridge this gap by reviewing recent developments in genetic programming and reinforcement learning approaches for job shop scheduling problems, providing a comparison in terms of the learning principles and characteristics for solving different kinds of job shop scheduling problems. In addition, this survey identifies and discusses current issues and challenges in the field of learning to optimise for job shop scheduling. This comprehensive exploration of genetic programming and reinforcement learning in job shop scheduling provides valuable insights into the learning principles for optimising different job shop scheduling problems. It deepens our understanding of recent developments, suggesting potential research directions for future advancements.