Artificial intelligence chatbot research has focused on technical advances in natural language processing and validating the effectiveness of human-machine conversations in specific settings. However, real-world chat data remain proprietary and unexplored despite their growing popularity, and new analyses of chatbot uses and their effects on mitigating negative moods are urgently needed. In this study, we investigated whether and how artificial intelligence chatbots facilitate the expression of user emotions, specifically sadness and depression. We also examined cultural differences in the expression of depressive moods among users in Western and Eastern countries. This study used SimSimi, a global open-domain social chatbot, to analyze 152,783 conversation utterances containing the terms "depress" and "sad" in 3 Western countries (Canada, the United Kingdom, and the United States) and 5 Eastern countries (Indonesia, India, Malaysia, the Philippines, and Thailand). Study 1 reports new findings on the cultural differences in how people talk about depression and sadness to chatbots based on Linguistic Inquiry and Word Count and n-gram analyses. In study 2, we classified chat conversations into predefined topics using semisupervised classification techniques to better understand the types of depressive moods prevalent in chats. We then identified the distinguishing features of chat-based depressive discourse data and the disparity between Eastern and Western users. Our data revealed intriguing cultural differences. Chatbot users in Eastern countries indicated stronger emotions about depression than users in Western countries (positive: P<.001; negative: P=.01); for example, Eastern users used more words associated with sadness (P=.01). However, Western users were more likely to share vulnerable topics such as mental health (P<.001), and this group also had a greater tendency to discuss sensitive topics such as swear words (P<.001) and death (P<.001). In addition, when talking to chatbots, people expressed their depressive moods differently than on other platforms. Users were more open to expressing emotional vulnerability related to depressive or sad moods to chatbots (74,045/148,590, 49.83%) than on social media (149/1978, 7.53%). Chatbot conversations tended not to broach topics that require social support from others, such as seeking advice on daily life difficulties, unlike on social media. However, chatbot users acted in anticipation of conversational agents that exhibit active listening skills and foster a safe space where they can openly share emotional states such as sadness or depression. The findings highlight the potential of chatbot-assisted mental health support, emphasizing the importance of continued technical and policy-wise efforts to improve chatbot interactions for those in need of emotional assistance. Our data indicate the possibility of chatbots providing helpful information about depressive moods, especially for users who have difficulty communicating emotions to other humans.