A symmetry of a physical system is a physical or mathematical feature of the system that is preserved or remains unchanged under some transformation. For example, the speed of light is an example of symmetry and its value will always will always remain the same no matter where and what coordinate system(e.g. cartesian, polar, etc) one use. But as for gauge symmetry, we can only only use one coordinate though we get to choose what coordinate system we use(gauge fixing?) and we can made the transition between different coordinate system. Is this what gauge symmetry? If it is, is it why gauge symmetry is not a symmetry cause we can't preserve invariance when we move between different coordinate system? Thanks for your help.