We analyse radial stellar metallicity and kinematic profiles out to 1Re in 244 CALIFA galaxies ranging from morphological type E to Sd, to study the evolutionary mechanisms of stellar population gradients. We find that linear metallicity gradients exhibit a clear correlation with galaxy morphological type - with early-type galaxies showing the steepest gradients. We show that the metallicity gradients simply reflect the local mass-metallicity relation within a galaxy. This suggests that the radial stellar population distribution within a galaxy's effective radius is primarily a result of the in situ local star formation history. In this simple picture, the dynamically derived stellar surface mass density gradient directly predicts the metallicity gradient of a galaxy. We show that this correlation and its scatter can be reproduced entirely by using independent empirical galaxy structural and chemical scaling relations. Using Schwarzschild dynamical models, we also explore the link between a galaxy's local stellar populations and their orbital structures. We find that galaxies' angular momentum and metallicity gradients show no obvious causal link. This suggests that metallicity gradients in the inner disc are not strongly shaped by radial migration, which is confirmed by the lack of correlation between the metallicity gradients and observable probes of radial migration in the galaxies, such as bars and spiral arms. Finally, we find that galaxies with positive metallicity gradients become increasingly common towards low mass and late morphological types - consistent with stellar feedback more efficiently modifying the baryon cycle in the central regions of these galaxies.