I think they are two different things - statistical modelling to me is about understanding relationships between data (i.e. we are highly confident that X and Y

I think they are two different things - statistical modelling to me is about understanding relationships between data (i.e. we are highly confident that X and Y are correlated, and can infer a reason and thus put a policy around that based on open reasoning), and ML is about making predictions in new situations based on historical training data from different situations (but we can't necessarily infer the why).