  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
($\Sigma_{\rm SFR}$), derived in Bluck et al. (2020), to compute the distance
at which each spaxel resides from the resolved star forming main sequence
($\Sigma_{\rm SFR} - \Sigma_*$ relation): $\Delta \Sigma_{\rm SFR}$. We study
galaxy radial profiles in $\Delta \Sigma_{\rm SFR}$, and luminosity weighted
stellar age (${\rm Age_L}$), 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 ($\sigma_c$) 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 $M_{BH}$ - $\sigma_c$ relation, we estimate
that quenching via AGN feedback must occur at $M_{BH} \geq 10^{6.5-7.5}
M_{\odot}$, and is marked by steeply rising $\Delta \Sigma_{\rm SFR}$ 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.
