Generative Artificial Intelligence (AI) tools, such as ChatGPT, are transforming how people approach complex creative and communicative tasks, including writing. While these tools are often seen as sources of inspiration and active contributors to the writing process, the question arises as to whether these perceptions vary across different writing contexts. In this study, we used two vignettes, each describing a fictional person experiencing emotional and cognitive challenges, to investigate how people interact with ChatGPT in two writing settings, which differed in their perspective of writing a counseling response (rational-analytical vs. emotional-supportive). Analyses of prompting behavior, content adoption from ChatGPT, time spent on the writing tasks, and ratings of own contribution to the text showed no significant interaction effects between perspective of writing and presented vignette and no main effects of perspective of writing. However, the analyses revealed significantly greater content adoption and more time spent on the second than on the first vignette. Linguistic feature analysis of the texts revealed a significantly greater average text length and a greater usage of affect-based (both only for the second vignette) and informal (across both vignettes) wording in the emotional-supportive than in the rational-analytical writing condition. In addition, there was a greater frequency of analytical wording in the rational-analytical than in the emotional-supportive writing condition across both vignettes. This study contributes to the field of human-AI co-creation by providing insights into interaction patterns of human-AI co-writing, with our results suggesting a similar approach to the use of AI for rational-analytical and emotional-supportive writing contexts.