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 (Σ SFR ), derived in Bluck et al. (2020), to compute the distance at which each spaxel resides from the resolved star forming main sequence (Σ SFR − Σ * relation): ∆Σ SFR . We study galaxy radial profiles in ∆Σ SFR , and luminosity weighted stellar age (Age L ), 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 (σ 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 (δ 5 ) being the most important single parameter. Utilising the empirical M BH -σ c relation, we estimate that quenching via AGN feedback must occur at M BH 10 6.5−7.5 M , and is marked by steeply rising ∆Σ 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∼0.1, and is marked by steeply declining ∆Σ 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.