In recent years, unmanned aerial vehicles (UAVs) have become increasingly popular in our daily lives and have attracted significant research interest in software engineering. At the same time, large language models (LLMs) have made notable advancements in language understanding, reasoning, and generation, making LLM applications in UAVs a promising research direction. However, existing studies have largely remained in preliminary exploration with a limited understanding of real-world practice, which causes an academia-industry gap and hinders the application of LLMs in UAVs. To address this, we conducted the first empirical study to investigate how LLMs support UAVs. To characterize common tasks and application scenarios of real-world UAV-LLM practices, we conducted a large-scale empirical study involving 997 research papers and 1,509 GitHub projects. The results classified nine common tasks (e.g., Natural Language Command Parsing) in four UAV workflows (e.g., Information Input) undertaken by LLMs in real-world UAV projects and revealed a large difference in the task distribution of research efforts and industry practices. To gain deeper insight into these differences and understand developers' perspectives on the application of LLMs in UAVs, we conducted a survey of practitioners, receiving 52 valid responses from 15 countries. The results revealed that while 40.4% of developers have attempted to apply LLMs to UAV tasks, 59.6% still face challenges integrating their UAV projects with advanced LLM capabilities. Their feedback attributes these challenges to five factors, including technological maturity, performance, safety, cost, and others, and provides practical implications for researchers and developers in conducting UAV-LLM practices.