We investigate how star formation quenching proceeds within central and satellite galaxies using spatially resolved spectroscopy from the SDSS-IV MaNGA DR15. We adopt a complete sample of star formation rate surface densities ($\Sigma SFR$), derived in Bluck et al. (2020), to compute the distance at which each spaxel resides from the resolved star forming main sequence ($\Sigma SFR-\Sigma \ast$ relation): $\Delta \Sigma SFR$. We study galaxy radial profiles in $\Delta \Sigma SFR$, and luminosity weighted stellar age ($AgeL$), split by a variety of intrinsic and environmental parameters. Via several statistical analyses, we establish that the quenching of central galaxies is governed by intrinsic parameters, with central velocity dispersion ($\sigma c$) being the most important single parameter. High mass satellites quench in a very similar manner to centrals. Conversely, low mass satellite quenching is governed primarily by environmental parameters, with local galaxy over-density ($\delta 5$) being the most important single parameter. Utilising the empirical $MBH$ - $\sigma c$ relation, we estimate that quenching via AGN feedback must occur at $MBH\ge 106.5-7.5M\odot$, and is marked by steeply rising $\Delta \Sigma SFR$ radial profiles in the green valley, indicating inside-out' quenching. On the other hand, environmental quenching occurs at over-densities of 10 - 30 times the average galaxy density at z$\sim$0.1, and is marked by steeply declining $\Delta \Sigma_{\rm SFR}$ profiles, indicating outside-in' quenching. Finally, through an analysis of stellar metallicities, we conclude that both intrinsic and environmental quenching must incorporate significant starvation of gas supply.