What does "predictive discrimination" mean and how is it different from classification? What does predictive discrimination mean and how is it different from classification?
My question is prompted by Frank Harrell's comment:

Predictive discrimination is much more general a concept than classification.
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This comment is at odds with my current thinking that predictive discrimination is simply an old-fashioned synonym for what is now called the supervised classification task. I would also assume that predictive discrimination is distinct from just discrimination, which could also mean clustering, depending on the context.
This term does not appear at all in books on machine learning that I usually use as a reference. Searching the web proved to be unproductive, as mostly sociopolitical applications of machine learning come up in the results.

Frank Harrell's comment [emphasis is mine]:

Predictive discrimination is the degree to which predictive signals can separate those with good outcomes from those with worse outcomes. The most popular measures of discrimination are R2 and c-index (concordance probability; equal to AUROC when Y is binary). Rank correlations between X and Y are measures of predictive discrimination. This is more general than classification as it takes into account tendencies/gray zones as in probability models. See https://fharrell.com/post/addvalue

His comparison of predictive discrimination to classification seems like apples and oranges to me, because the former is a statistic or performance measure, while the latter is a task or a problem setting. But this will do.
