The dense environment of galaxy clusters strongly influences the nature of galaxies. Here, we study the cause of the size distribution of a sample of 560 spectroscopic members spanning a wide dynamical range down to 10^8.5 M_sol (log(M)-2) in the massive CLASH cluster MACSJ 1206.2-0847 at z~0.44. We use Subaru SuprimeCam imaging covering the highest-density core out to the infall regions (3 virial radii) to look for cluster-specific effects. We also compare our measurements to a compatible large field study in order to span extreme environmental densities. This paper presents the trends we identified for cluster galaxies divided by their colors into star-forming and quiescent galaxies and into distinct morphological types (using S\'ersic index and bulge/disk decompositions). We observed larger sizes for early type and smaller sizes for massive late type galaxies in clusters in comparison to the field. We attribute this to longer quenching timescales of more massive galaxies in the cluster. Our analysis further revealed an increasing importance of recently quenched transition objects ("red disks"). This is a virialized population found at higher cluster-centric radii with sizes similar to the quiescent, spheroid-dominated population of the cluster center, but with disks still in-tact. The mass-size relation of cluster galaxies may therefore be understood as the consequence of a mix of progenitors formed at different quenching epochs. We also find that galaxy sizes smoothly decreasing as a function of bulge fraction. At same bulge-to-total ratio and same stellar mass, quiescent galaxies are smaller than star-forming galaxies. This is likely because of a fading of the outskirts of the disk, which we saw in comparing sizes of their disk-components. Ram-pressure stripping of the cold gas and other forms of more gradual gas starvation are likely responsible for this observation.