  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]
