No, it isn't the same thing. The softmax probabilities are estimates; they're part of the prediction. The other poster is talking about the uncertainty in these estimates, so the uncertainty in the softmax probabilities.

The softmax probabilities are usually not a very good indication of uncertainty, as the model is often overconfident due to neural collapse. The uncertainty in the softmax probabilities is a good indication though, and can be used to detect out-of-distribution entries or poor predictions.