Generative AI for the creation of images is becoming a staple in the toolkit of digital artists and visual designers. The interaction with these systems is mediated by \emph{prompting}, a process in which users write a short text to describe the desired image's content and style. The study of prompts offers an unprecedented opportunity to gain insight into the process of human creativity. Yet, our understanding of how people use them remains limited. We analyze more than 145,000 prompts from the logs of two Generative AI platforms (Stable Diffusion and Pick-a-Pic) to shed light on how people \emph{explore} new concepts over time, and how their exploration might be influenced by different design choices in human-computer interfaces to Generative AI. We find that users exhibit a tendency towards exploration of new topics over exploitation of concepts visited previously. However, a comparative analysis of the two platforms, which differ both in scope and functionalities, reveals some stark differences. Features diverting user focus from prompting and providing instead shortcuts for quickly generating image variants are associated with a considerable reduction in both exploration of novel concepts and detail in the submitted prompts. These results carry direct implications for the design of human interfaces to Generative AI and raise new questions regarding how the process of prompting should be aided in ways that best support creativity.