"Although I more or less agree with that definition my personal view of Generative Design is slightly different. For lack of a better example I'm going to go with DNA. In its raw state, DNA contains all of the instructions by which life can be created. It will dictate the growth of cells as well as the type/characteristics of cells. Theoretically you could clone someone from their DNA and get an exact "copy" of that person (remember Dolly?). However, the end result of that clone would not be an exact copy. Why? The growth of cells is not dictated solely by DNA, but also by its interactions with its surroundings. Since the clone invariably develops in conditions that were different from the "source being" there will always be a difference between the two.
To me, this is the characteristic of generative design. Its not just a product of the parameters that generate it, but of the conditions that surround and interact with it. Even within that definition, there's a very thin line that separates parametric design from generative design, since both rely on defining their operations through external values. That thin line, to me, is parametric design being generated by a singular reference to an outside piece of data and generative design being generated by a multitude of references an some interpretation of those references in an interconnected manner.
I've moved towards defining GH as a Logical Modeler rather than parametric or generative. The main reason is that most parametric modelers rarely focus on the link between parameters as an artifact of their process. Because of this, their process, though parametrically based, is still embedded within model itself, which is certainly fine. GH does not operate in this manner. The creation of a GH definition is more of a representation of the logical steps used to create a given output, where as with parametric modelers, the representation of the inheritance of all parameters is not nearly as evident. Considering the control, amount of information that is immediately available by looking at a definition, and the interaction with those logical steps I would certainly argue that THAT is an extremely valuable aspect of the GH process. I could possibly argue that the GH definition itself is more valuable than the output it creates.
As to the Generative capabilities of parametric modelers and GH, it all depends on how you structure the interactions with external data. A 1 to 1 relationship between a value and an output is more parametric in my book, where the interaction between a multitude of values is more of a generative approach.
Just my 2 cents "
Best, Damien