(1) The mathematical model can be said to be a mathematical equation, and the more complicated one can be a partial differential equation, such as the vibration equation involving single degree of freedom and multiple degrees of freedom in vibration analysis. Even if this is a mathematical model, there are mathematical modeling competitions in universities now. In fact, in the final analysis, it still depends on what mathematical means you use to solve it, so it is a bit narrow to say what mathematical means you want to use to realize the mathematical model.

(2) Compared with mathematical model, the most important feature of physical model is "image". For example, the model established by finite element software such as ANSYS and Patran, even the physical model, because it is visible in the image, is like a simplification of the actual object, but the physical model is essentially composed of mathematical equations, only hidden in the computer, showing us the simplified structure of the image.

The above is just my personal understanding, please correct me if there is anything wrong!