Context: According to numerical simulations, stars are not always kept at their birth galactocentric distances but migrate. The importance of this radial migration in shaping galactic light distributions is still unclear. However, if it is indeed important, galaxies with different surface brightness (SB) profiles must display differences in their stellar population properties. Aims: We investigate the role of radial migration on the light distribution and the radial stellar content by comparing the inner colour, age and metallicity gradients for galaxies with different SB profiles. We define these inner parts avoiding the bulge and bar regions and up to around three disc scale-lengths (type I, pure exponential) or the break radius (type II, downbending; type III, upbending). Methods: We analyse 214 spiral galaxies from the CALIFA survey covering different SB profiles. We make use of GASP2D and SDSS data to characterise their light distribution and obtain colour profiles. The stellar age and metallicity profiles are computed using a methodology based on full-spectrum fitting techniques (pPXF, GANDALF, and STECKMAP) to the IFS CALIFA data. Results: The distributions of the colour, stellar age and stellar metallicity gradients in the inner parts for galaxies displaying different SB profiles are unalike as suggested by Kolmogorov-Smirnov and Anderson-Darling tests. We find a trend in which type II galaxies show the steepest profiles of all and type III the shallowest, with type I galaxies displaying an intermediate behaviour. Conclusions: These results are consistent with a scenario in which radial migration is more efficient for type III galaxies than for type I systems with type II galaxies presenting the lowest radial migration efficiency. In such scenario, radial migration mixes the stellar content flattening the radial stellar properties and... [abriged]
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