By means of the fossil record method implemented through Pipe3D, we reconstruct the global and radial stellar mass growth histories (MGHs) of an unprecedentedly large sample of galaxies, ranging from dwarf to giant objects, from the "Mapping Nearby Galaxies at the Apache Point Observatory" survey. We confirm that the main driver of the global MGHs is mass, with more massive galaxies assembling their masses earlier (downsizing), though for a given mass, the global MGHs segregate by color, specific star formation rate (sSFR), and morphological type. From the inferred radial mean MGHs, we find that at the late evolutionary stages (or for fractions of assembled mass larger than ~ 80%), the innermost regions formed stars on average earlier than the outermost ones (inside-out). At earlier epochs, when the age resolution of the method becomes poor, the mass assembly seems to be spatially homogeneous or even in the outside-in mode, specially for the red/quiescent/early-type galaxies. The innermost MGHs are in general more regular (less scatter around the mean) than the outermost ones. For dwarf and low-mass galaxies, we do not find evidence of an outside-in formation mode; instead their radial MGHs are very diverse most of the time, with periods of outside- in and inside-out modes (or strong radial migration), suggesting this an episodic SF history. Blue/star-forming/late-type galaxies present on average a significantly more pronounced inside-out formation mode than red/quiescent/early-type galaxies, independently of mass. We discuss our results in the light of the processes of galaxy formation, quenching, and radial migration. We discuss also on the uncertainties and biases of the fossil record method and how they could affect our results.