  We use the Auriga simulations to probe different satellite quenching
mechanisms operating at different mass scales ($10^5 M_\odot \lesssim M_\star
\lesssim 10^{11} M_\odot$) in Milky Way-like hosts. Our goal is to understand
the origin of the satellite colour distribution and star-forming properties in
both observations and simulations. We find that the satellite populations in
the Auriga simulations, which was originally designed to model Milky Way-like
host galaxies, resemble the populations in the Exploration of Local VolumE
Satellites (ELVES) Survey and the Satellites Around Galactic Analogs (SAGA)
survey in their luminosity function in the luminosity range $-12 \lesssim M_V
\lesssim -15$ and resemble ELVES in their quenched fraction and
colour--magnitude distribution in the luminosity range $-12 \lesssim M_g
\lesssim -15$. We find that satellites transition from blue colours to red
colours at the luminosity range $-15 \lesssim M_g \lesssim -12$ in both the
simulations and observations and we show that this shift is driven by
environmental effects in the simulations. We demonstrate also that the colour
distribution in both simulations and observations can be decomposed into two
statistically distinct populations based on their morphological type or
star-forming status that are statistically distinct. In the simulations, these
two populations also have statistically distinct infall time distributions. The
comparison presented here seems to indicate that the tension between the
quenched fraction in SAGA and simulations is resolved by the improved target
selection of ELVES, but there are still tensions in understanding the colours
of faint galaxies, of which ELVES appears to have a significant population of
faint blue satellites not recovered in Auriga.
