Physical laws(or knowledge model) give you an accurate model of the system but this model is generally complexe so we can simplify this model by reduction technics allowing to have an equivalent model more suitable to control (generally a 2nd order is satisfactory) . It's important to notice that one of the objectives of control is to accelerate slow dynamics (dominant poles) so we don't need to know with precision fast dynamics.
The control model can also be obtained by identification of an input output model (generally a second order). so both approaches can be used for control.