I might very well have my terms mixed up - I'm by no means well-versed in this type of engineering. (Yet?) My understanding of parametric is that it is a relational method of design; thing A's size depends on thing B. It can be made much more complex than that, and it can be types of "inputs A should lead to shapes B constrained by strenght model C and solution space D", but fundamentally it's about the relationships between design elements. Could've made that clearer, I suppose, or I'm missing something. Generative design as I have dabbled with is "given input parameters A that each can vary this amount, and given model B that takes these parameters and generates a design, measure set of result-based KPIs C and iterate over A to optimize C."
In mechanics, you're talking about parametric design; Solidworks and Fusion will do it all day long. "The distance from A to B is 1/2 the distance from B to C." Move C, A will move. Those interdependencies allow you to change things up pretty easily if you set your model up right. Generative design in mechanics runs exactly as you describe, but the goals are different: "Given torsion forces A, B and C, compressive forces D, E and F, shear G H and I and clamping forces J and K, generate a continuous cross-section between pins Alpha-Beta and holes Gamma-Theta that minimizes the weight of the assembly. Presume a Young's Modulus of x, a shear modulus of y, a density of z and a factor of safety of five now GO." Things had to get computationally intensive to do this. you're goal-seeking through finite element analysis which, back when I had to do it, took ten minutes of server time on a DEC Alpha just to model a bike frame made of constant-diameter tube.