Neither of those words are very specific, and everyone in the LLM space knows that "reasoning" tokens are just tokens that don't appear in the answer shown to the user.
Non-technical people believing that these models are actually thinking can lead to all sorts of inappropriate uses.
The problem is that the language spills outside of the LLM space, so we should use terminology which is more generally understood in a way which reflects reality.
- It conveys the idea that they aren't tokens normally visible or part of the final answer.
- It conveys the idea that the longer the models "reasons", the better the output.
What other term best describes both of these ideas? Why should we use a less useful terms just because it can confuse some people? I mean, some in 1952 feared that calling computer memory "memory" was already too much anthropomorphization[1]!