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Rapid rescore is used in the mortgage space to trigger a balance update from lenders such that a pull can happen again with prettier balances (hopefully).
Might be used in other loan types too, but they're still point in time pulls, not sure what you're referring to on old data... as far as a RR goes, it's either there or it's not.

A new score that is obtained after removal of prior information, such as a derog, no longer includes the effect of that information in the scoring calculation, regardless of whether it was removed because it was inaccurate or because it was voluntarily deleted..
Scoring does not involve any "backdating" to a prior date. It is based on the current credit report after change in reported information.