We present a study on the star formation histories (SFHs) of galaxies covering the range 104 < M⋆/M⊙ < 1012, leveraging full spectral fitting algorithms. Our sample consists of 31 dwarf galaxies from the SAMI-Fornax Survey with stellar masses between 107-$10^{9.5} \, {\rm M}_{\odot }$, early-type galaxies from the ATLAS3D project with stellar masses between 1010-$10^{12} \, {\rm M}_{\odot }$, and dwarf galaxies that are satellites of Andromeda and the Milky Way, with 104 < M⋆/M⊙ < 108. We find that galaxies from 107-$10^{8} \, {\rm M}_{\odot }$ exhibit the smallest star formation rates (SFRs), while the SFR increase as we move down or up in mass. In this sense, we find that some $10^{5} \, {\rm M}_{\odot }$ galaxies have cumulative SFHs that are comparable to those of $10^{12} \, {\rm M}_{\odot }$ galaxies. Our study shows that the evolution of giant galaxies is primarily governed by their internal properties, with time-scales that do not depend on their environmental location. In contrast, dwarf galaxies below $10^{8} \, {\rm M}_{\odot }$ can be significantly affected in dense environments, such as the inner regions of a cluster, that severely quench the galaxies before the assembly of their 50 per cent present-day mass. We find that, only dwarfs with stellar masses between 107-$10^{9} \, {\rm M}_{\odot }$ actively form stars nowadays, while less massive galaxies seem to remain unaffected by the environment due to the expulsion of most of their gas at an early stage in their evolution. Our study highlights and corroborates a critical threshold around $10^{8}-10^{9} \, {\rm M}_{\odot }$ in galaxy evolution from previous studies, separating more massive galaxies minimally impacted by the environment from those less massive galaxies quenched by it.