I believe that your basic question is the difference between a variable and a parameter.

Many math instructors are rather loose with the vocabulary; in particular they will define a variable as a letter/symbol taking the place of a number. But there is a difference between a physical constant, a constant, a parameter, and a variable.

A physical/mathematical constant is a number that arises in particular applications so often that we represent it with a letter/symbol. Thus `pi,phi` in math, or c for the speed of light, etc... are constants.

Other constants aren't as prevalent or have a specific utilization. Specific substances have a specific boiling point, measure of elasticity, albedo, etc...

A variable is allowed to change within the application/procedure/algorithm. Thus we are allowed to change "x" in an algebraic equation and "y" will then possible change.

A parameter does not change in a specific application, but takes on different values from application to application. Pythagoras's theorem `a^2+b^2=c^2` applies to all right triangles, but are unchanged if you are give a specific triangle.

A good example of parameters at work is the equation for a parabola. `y=ax^2+bx+c` ; for a specific parabola a,b, and c remain unchanged while x and y are allowed to change.