I know what gauge invariance is, but I'm not sure what gauge covariance is. Is it that a given field has a gauge covariant derivative? And under which circumstances do we get a field that is gauge invariant but not gauge covariant? And I would appreciate an example (other than the one below). Finally, what is the link between gauge covariance and QCD? I'm asking because I read that the Pauli Villars regulator is not gauge covariant (which I don't understand what it means) hence can't be used in QCD. Could someone clear the confusion fog in my head, please?