To meet the evolving demands of sixth-generation (6G) wireless channel modeling, such as precise prediction capability, extension capabilities, and system participation capability, multi-modal intelligent channel modeling (MMICM) has been proposed based on Synesthesia of Machines (SoM) which explores the mapping relationship between multi-modal sensing in physical environment and channel characteristics in electromagnetic space. Furthermore, for integrating heterogeneous sensing, reasoning across scales, and generalizing to complex air-space-ground-sea communication environments, two new paradigms of MMICM are explored, including fine-tuned large language models (LLMs) for Channel Modeling (LLM4CM) and Wireless Channel Foundation Model (WiCo). LLM4CM leverages pre-trained LLMs on channel representations for cross-modal alignment and lightweight adaptation, enabling flexible channel modeling for 6G multi-band and multi-scenario communication systems. WiCo, which pre-trained on physically valid channel realizations and their associated environmental and modal observations, embeds electromagnetic equations for physical interpretability and uses parameterized adapters for scalability. This article details the architectures and features of LLM4CM and WiCo, laying a foundation for artificial intelligence (AI)-native 6G wireless communication systems. Then, we conducts a comparative analysis of the two emerging paradigms, focusing on their distinct characteristics, relative advantages, inherent limitations, and performance attributes. Finally, we discuss the future research directions.