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© ESO, 2017. Artículo firmado por 24 autores. We thank the referee for very useful suggestions and comments that have helped improve the current version of this manuscript. The authors also thank L. Coccato and M. Sarzi for the new version of the GANDALF code taking into account the dependency with wavelength of the instrumental FWHM. We would like to thank Reynier Peletier and Stephane Courteau for very helpful suggestions and discussions that have considerably improved this paper. This paper is (partially) based on data obtained by the CALIFA Survey, funded by the Spanish Ministery of Science under grant ICTS-2009-10, and the Centro Astronómico Hispano-Alemán. T.R.L. thanks the support of the Spanish Ministerio de Educación, Cultura y Deporte by means of the FPU fellowship. This research has been supported by the Spanish Ministry of Science and Innovation (MICINN) under grants AYA2014-53506-P, AYA2007-67625-C02-02, AYA2014-56795-P and Consolider-Ingenio CSD2010-00064; and by the Junta de Andalucía (FQM-108). L.G. was supported in part by the US National Science Foundation under Grant AST-1311862. I.M. would like to thank support under grants AYA2013-42227-P and AYA2016-76682-C3-1-P. S.Z. has been supported by the EU Marie Curie Career Integration Grant SteMaGE No. PCIG12-GA-2012-326466 (Call Identifier: FP7-PEOPLE-2012 CIG). J.F.B. thanks the support received under grant AYA2016-77237-C3-1-P. A.d.L.C. acknowledges support from the CONACyT-125180, DGAPA-IA100815 and DGAPA-IA101217 projects. R.A.M. acknowledges support by the Swiss National Science Foundation. J.M.A. thanks support from the support from the European Research Council Starting Grant (SEDmorph; P.I. V. Wild) and MINECO through the grant AYA2013-43188-P. Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the US Department of E, Context. According to numerical simulations, stars are not always kept at their birth galactocentric distances but they have a tendency to migrate. The importance of this radial migration in shaping galactic light distributions is still unclear. However, if radial migration 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 in the light distribution and 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 analysed 214 spiral galaxies from the CALIFA survey covering different SB profiles. We made use of GASP2D and SDSS data to characterise the light distribution and obtain colour profiles of these spiral galaxies. The stellar age and metallicity profiles were computed using a methodology based on full-spectrum fitting techniques (pPXF,GANDALF, and STECKMAP) to the Integral Field Spectroscopic 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, type III show the shallowest, and type I display 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, where type II galaxies present the lowest radial migration efficiency. In such a scenario, radial migration mixes the stellar content, thereby flattening the radial stellar properties and shaping different SB profiles. However, Unión Europea. FP7, Ministerio de Ciencia e Innovación (MICINN), Ministerio de Educación, Cultura y Deporte (MECD), Centro Astronómico Hispano-Alemán, Junta de Andalucía, US National Science Foundation, Swiss National Science Foundation, European Research Council Starting Grant (SEDmorph), Alfred P. Sloan Foundation, National Aeronautics and Space Administration, National Science Foundation, US Department of Energy, Japanese Monbukagakusho, Max Planck Society, Depto. de Física de la Tierra y Astrofísica, Fac. de Ciencias Físicas, TRUE, pub