It's worth pointing out that credit scores actually are actually just the P(^default) expressed on an integer rather than fractional scale.
There's also multiple credit scores, there are the scores computed by credit bureaus which look at your P(default) against all lenders, but many lenders also compute their own internal credit scores using models trained against their own customer base (and possibly also taking into account additional data that they hold about you).
It's worth pointing out that credit scores actually are actually just the P(^default) expressed on an integer rather than fractional scale.
There's also multiple credit scores, there are the scores computed by credit bureaus which look at your P(default) against all lenders, but many lenders also compute their own internal credit scores using models trained against their own customer base (and possibly also taking into account additional data that they hold about you).