Since the launch of ChatGPT in 2022, an increasing number of ChatGPT-related projects are being published on GitHub, sparking widespread discussions. However, GitHub does not provide a detailed classification of these projects to help users effectively explore interested projects. Additionally, the issues raised by users for these projects cover various aspects, e.g., installation, usage, and updates. It would be valuable to help developers prioritize more urgent issues and improve development efficiency. We retrieved 71,244 projects from GitHub using the keyword `ChatGPT' and selected the top 200 representative projects with the highest numbers of stars as our dataset. By analyzing the project descriptions, we identified three primary categories of ChatGPT-related projects, namely ChatGPT Implementation & Training, ChatGPT Application, ChatGPT Improvement & Extension. Next, we applied a topic modeling technique to 23,609 issues of those projects and identified ten issue topics, e.g., model reply and interaction interface. We further analyzed the popularity, difficulty, and evolution of each issue topic within the three project categories. Our main findings are: 1) The increase in the number of projects within the three categories is closely related to the development of ChatGPT; and 2) There are significant differences in the popularity, difficulty, and evolutionary trends of the issue topics across the three project categories. Based on these findings, we finally provided implications for project developers and platform managers on how to better develop and manage ChatGPT-related projects.