Although AI-powered chatbots are widely used to deliver personalized services across various digital platforms, utilitarian and hedonic motivations remain two fundamental driving factors behind their adoption. However, research on how to design chatbots based on different user motivations remains limited. The current study investigates the impact of chatbot appearance (human-like vs. animal-like vs. machine-like) and social cues (absent vs. present) on user perceptions under both utilitarian and hedonic motivations. A total of 42 participants completed utilitarian-oriented and hedonic-oriented conversational tasks with chatbots powered by generative AI technologies, each featuring different designs. The results revealed that performing utilitarian tasks significantly increased the perceived competence of the chatbots, whereas performing hedonic tasks significantly increased the perceived warmth. In addition, human-like appearances were perceived as the most competent and satisfying compared to animal-like or machine-like appearances. Social cues were found to have interaction effects with user motivations. Specifically, participants reported lower levels of perceived competence for chatbots with social cues in utilitarian contexts, whereas they experienced higher levels of frustration with social cues in hedonic contexts. The findings suggest that the design of chatbots is significantly influenced by the context in which they are used. The alignment between the task’s features and the chatbot’s attributes plays a critical role in shaping user perceptions, thereby enhancing the overall user experience in different contexts. Practical guidance for chatbot design is also provided in this study.