Propensity score matching (and other matching techniques) are used, as far as I have seen, exclusively for identifying causal effects of a treatment (intervention) and particularly where there is a suspicion of selection bias.
However I do not see why they might not be useful for other cases of comparing two groups within a sample. E.g. I am looking at differences between rural-to-urban migrants and urban natives in education outcomes. It makes little sense to see this as a 'treatment' effect (although it might if I was comparing rural-to-urban migrants with rural natives), and causation is not exactly the issue. I want to understand whether there is a difference that can be explained by migration status separately from that explained by differences between migrants and urban natives in terms of wealth, parents' education and other observed variables.
This would usually be done using linear regression and ordinary least squares. But wouldn't there be some advantages to using a matching technique here? Specifically, doesn't OLS apply the same linear relationships among covariates to the whole sample, while matching could better allow for variation in those relationships? In this type of case, would matching perhaps be comparable to regression with lots of interaction effects allowed among the covariates?
(I am aware of this earlier question but everything I come across on matching seems to assume you are trying to evaluate causal effects of a treatment. It would be great to hear about any counter-examples to my claim that matching is only ever used for treatment effects, if there are any.)