'slow' means making one or several action-dependent forecasts, evaluating the expected value of the outcomes, and making a decision based on that.

Neither map exactly to the situation with LLMs, but very roughly, the first is analogous to trained classifiers and the second to reasoning models.

The analogy breaks down, since each instance of token being produced is an example of a policy execution (system 1), and reasoning is just stringing lots of these together. But there are those who argued, before LLMs, that system 2 is just "policy composition" anyway...