Wikipedia mentions at least three different interpretations of the term: https://en.wikipedia.org/wiki/Data_generating_process
It seems to have a specific meaning in econometrics, from which the acronym DGP appears to be derived, see for example here or here, or even more generally in the context of regression, where the population regression function PRF is a feature of the DGP.
However, vaguer usage of the term, similar to the first definition give in Wikipedia ("the data-collection process") also seems to be used elsewhere, e.g. here.
In what sense is it supposed to be used on CrossValidated? I.e., what should be its usage guidelines?