Personally, I think the coordinate system is a model tool for science and engineering research. The coordinate system used in high school is mostly Cartesian coordinate system. The purpose of introducing coordinate system is to solve an abstract mathematical and physical problem quantitatively.

Let's talk about the difference between mathematical coordinate system and high school physical coordinate system. In essence, I think it's all the above coordinate system, and the difference is not big. However, in specific problems, the usage may be different: the mathematical coordinate system is more abstract than the physical coordinate system: the mathematical coordinate system is generally used to study functions, so the abscissa is used as an independent variable (generally set as X) and the ordinate is used as a dependent variable (generally set as Y) to reflect the function image and its related changes; In physics, the establishment of coordinate system may only describe the motion state of objects, such as displacement, velocity and acceleration. After the establishment of the coordinate system, the physical quantities in the coordinate system are described in mathematical language. The introduction of coordinate system can make physical quantities abstract and easy to study.

To sum up, I think there is no difference between the two in essence, but the occasions of use are different, so the expression and the steps of use are slightly different.