Researches on leveraging big artificial intelligence model (BAIM) technology to drive the intelligent evolution of wireless networks are emerging. However, since the breakthrough in generalization brought about by BAIM techniques mainly occurs in natural language processing, there is still a lack of a clear technical roadmap on how to efficiently apply BAIM techniques to wireless systems with many additional peculiarities. To this end, this paper first reviews recent research works on BAIM for wireless and assesses the current research situation. Then, this paper analyzes and compares the differences between language intelligence and wireless intelligence on multiple levels, including scientific foundations, core usages, and technical details. It highlights the necessity and scientific significance of developing BAIM technology in a wireless-native way, as well as new issues that need to be considered in specific technical implementation. Finally, by synthesizing the evolutionary laws of language models with the particularities of wireless system, this paper provides several instructive methodologies for how to develop wireless-native BAIM.