Current comparisons of large reasoning models (LRMs) focus on macro-level statistics such as task accuracy or reasoning length. Whether different LRMs reason differently remains an open question. To address this gap, we introduce the LLM-proposed Open Taxonomy (LOT), a classification method that uses a generative language model to compare reasoning traces from two LRMs and articulate their distinctive features in words. LOT then models how these features predict the source LRM of a reasoning trace based on their empirical distributions across LRM outputs. Iterating this process over a dataset of reasoning traces yields a human-readable taxonomy that characterizes how models think. We apply LOT to compare the reasoning of 12 open-source LRMs on tasks in math, science, and coding. LOT identifies systematic differences in their thoughts, achieving 80-100% accuracy in distinguishing reasoning traces from LRMs that differ in scale, base model family, or objective domain. Beyond classification, LOT's natural-language taxonomy provides qualitative explanations of how LRMs think differently. Finally, in a case study, we link the reasoning differences to performance: aligning the reasoning style of smaller Qwen3 models with that of the largest Qwen3 during test time improves their accuracy on GPQA by 3.3-5.7%.