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The emergence of new services and applications in emerging wireless networks (e.g., beyond 5G and 6G) has shown a growing demand for the usage of artificial intelligence (AI) in the Internet of Things (IoT). However, the proliferation of massive IoT connections and the availability of computing resources distributed across future IoT systems have strongly demanded the development of distributed AI for better IoT services and applications. Therefore, existing AI-enabled IoT systems can be enhanced by implementing distributed machine learning (aka distributed learning) approaches. This work aims to provide a comprehensive survey on distributed learning for IoT services and applications in emerging networks. In particular, we first provide a background of machine learning and present a preliminary to typical distributed learning approaches, such as federated learning, multi-agent reinforcement learning, and distributed inference. Then, we provide an extensive review of distributed learning for critical IoT services (e.g., data sharing and computation offloading, localization, mobile crowdsensing, and security and privacy) and IoT applications (e.g., smart healthcare, smart grid, autonomous vehicle, aerial IoT networks, and smart industry). From the reviewed literature, we also present critical challenges of distributed learning for IoT and propose several promising solutions and research directions in this emerging area.