The transition from 5G networks to 6G highlights a significant demand for machine learning (ML). Deep learning models, in particular, have seen wide application in mobile networking and communications to support advanced services in emerging wireless environments, such as smart healthcare, smart grids, autonomous vehicles, aerial platforms, digital twins, and the metaverse. The rapid expansion of Internet-of-Things (IoT) devices, many with limited computational capabilities, has accelerated the development of tiny machine learning (TinyML) and resource-efficient ML approaches for cost-effective services. However, the deployment of large-scale machine learning (LargeML) solutions require major computing resources and complex management strategies to support extensive IoT services and ML-generated content applications. Consequently, the integration of TinyML and LargeML is projected as a promising approach for future seamless connectivity and efficient resource management. Although the integration of TinyML and LargeML shows abundant potential, several challenges persist, including performance optimization, practical deployment strategies, effective resource management, and security considerations. In this survey, we review and analyze the latest research aimed at enabling the integration of TinyML and LargeML models for the realization of smart services and applications in future 6G networks and beyond. The paper concludes by outlining critical challenges and identifying future research directions for the holistic integration of TinyML and LargeML in next-generation wireless networks.