A lot of elementary statistical and econometric literature bases on so called "population models". An example is econometric handbook "Introductory Econometrics: A Modern Approach" by J. M. Wooldridge. or very influential paper of P. W. Holland "Statistics and Causal Inference".
On the other hand, some, especially new papers in Causal Infrence, instead to population refer to Data-Generating Process (DGP). An example could be "The Identification Zoo: Meanings of Identification in Econometrics" by A. Lewbel.
My understanding of that matter is that those concepts are very closely related, close enough to think of them as one thing. Of course they are not exactly the same entity, and population could be understood as an infinite number of units generated by particular DGP. Such understanding is derived from idea to join this two approaches.
As I am not strongly convinced to this, I would like to ask: What are the differences and similarities between Population and DGP as the bases of statistical and econometric modelling? And also, relatedly: What is the relation between these two concepts?