When one studies mathematics, one knows that a mathematical theory starts from axioms and then mathematics is used to prove theorems. When axioms change, the theory changes. A good example is Euclidean Geometry versus spherical geometry. Also in mathematics, a theorem may be used as an axiom, and the original axiom proven as a theorem.
Physics theories use mathematics as a tool to describe the natural world. But the mathematics of differential equations used extensively in physics, have an infinity of solutions and forms. It is necessary to use new "axioms" in order to pick up those solutions that are relevant to measurements and observations. These physics "axioms" are called "laws" "postulates" "principles" and are extracted from many observations and measurements so that the physics theory not only fits the data,but, very important, predicts new situations. (Just fitting data makes a mathematical map). At the same time there are at the level of axioms statements identifying the objects measured, mass, charge, (plus a lot of quantum numbers for particles)
Take $F=ma$ for example. It is a law, because when using it axiomatically ( together with the other two) Newtonian mechanics theory works beautifully, from predicting the planetary system, to trajectories of rockets , to stability of buildings etc.
The concept of force and mass existed in everyday language, because of the need to quantify products and the need to quantify effort, both everyday manifestations. The brilliant use though of the relation between acceleration , mass, and force brought the existence a complete and self consistent theoretical model for describing nature.