  Large language models appear quite creative, often performing on par with the
average human on creative tasks. However, research on LLM creativity has
focused solely on \textit{products}, with little attention on the creative
\textit{process}. Process analyses of human creativity often require hand-coded
categories or exploit response times, which do not apply to LLMs. We provide an
automated method to characterise how humans and LLMs explore semantic spaces on
the Alternate Uses Task, and contrast with behaviour in a Verbal Fluency Task.
We use sentence embeddings to identify response categories and compute semantic
similarities, which we use to generate jump profiles. Our results corroborate
earlier work in humans reporting both persistent (deep search in few semantic
spaces) and flexible (broad search across multiple semantic spaces) pathways to
creativity, where both pathways lead to similar creativity scores. LLMs were
found to be biased towards either persistent or flexible paths, that varied
across tasks. Though LLMs as a population match human profiles, their
relationship with creativity is different, where the more flexible models score
higher on creativity. Our dataset and scripts are available on
\href{https://github.com/surabhisnath/Creative_Process}{GitHub}.
