I think the most useful word in both cases is "extrapolating".

An LLM extrapolates from its context window to the immediate next token. This word applies whether you view what's happening as "reasoning", "prediction", or as a math function.

No, those aren't synonyms at all.

If I steer a car to avoid a predicted collision with a wall, this is not me 'predicting' the car. I am steering the car based on a prediction.