I am having some trouble understanding exactly what is meant by a DGP. Let's say it is stated that "the DGP is given as $y=a+bx+e$ where the error term fulfills all the OLS assumptions. Does this mean

a) Given knowledge of the value $x$ takes one would describe their belief about the value $y$ takes with the probability distribution on the right hand side.

b)something that allows a causal interpretation?

edit: in Econometric Theory and Methods by Davidson and Mckinnon on page 17 it is written that "the model(1.01) can be interpreted as a model for the mean of y conditional on x." To me this seems to say that the "true" regression model means what I say in a).

On Page 114 it is written(slightly summarised) "Let us suppose the model we estimate is $y=a+bx+e$ but that the DGP is $y=a+bx+cz+e$ this will yield biased estimates if $x$ and z are correlated".
I don't get what this is supposed to mean if the regression equation describes the mean of y conditional on x. The "underspecified" model will yield a higher(or lower) coefficient to take into account the correlation, it will however still correctly describe the expectation of $y$ conditional on x. Here it seems to me that they are interpreting the regression coefficients as meaning the expected change in y if the regressor is changed by one unit(in a specific instance)