The distinct evolutionary processes undergone by central and satellite galaxies are expected to have an impact on their observed statistical properties. In this work, we combine size and stellar mass measurements from the Sloan Digital Sky Server (SDSS) with the group finder algorithm of Rodriguez & Merchán in order to determine the stellar and halo mass - size relations of central and satellite galaxies separately. We show that, while central and satellite galaxies display similar stellar mass - size relations, their halo mass - size relations differ significantly. As expected, more massive haloes tend to host larger central galaxies. However, the size of satellite galaxies depends only slightly on halo virial mass. We show that these results are compatible with a remarkably simple model in which the size of central and satellite galaxies scales as the cubic root of their host halo mass, with the normalization for satellites being $\sim$30 % smaller than that for central galaxies which can be attributed to tidal stripping. We further check that our measurements are in excellent agreement with predictions from the IllustrisTNG hydrodynamical simulation. In the second part of this paper, we analyse how the clustering properties of central and satellite galaxies depend on their size. We demonstrate that, independently of the stellar mass threshold adopted, smaller galaxies are more tightly clustered than larger galaxies when either the entire sample or only satellites are considered. The opposite trend is observed on large scales when the size split is performed for the central galaxies alone. Our results place significant constraints for halo - galaxy connection models that link galaxy size with the properties of their hosting haloes.