  We present a spatially-resolved excitation analysis for the central molecular
zone (CMZ) of the starburst galaxy NGC 253 using the data from the ALMA Large
program ALCHEMI, whereby we explore parameters distinguishing NGC 253 from the
quiescent Milky Way's Galactic Center (GC). Non-LTE analyses employing a
hierarchical Bayesian framework are applied to Band 3-7 transitions from nine
molecular species to delineate the position-position-velocity distributions of
column density ($N_\mathrm{H_2}$), volume density ($n_\mathrm{H_2}$), and
temperature ($T_\mathrm{kin}$) at 27 pc resolution. Two distinct components are
detected: a low-density component with $(n_\mathrm{H_2},\
T_\mathrm{kin})\sim(10^{3.3}\ \mathrm{cm}^{-3}, 85 K)$ and a high-density
component with $(n_\mathrm{H_2},\ T_\mathrm{kin})\sim (10^{4.4}\
\mathrm{cm}^{-3}, 110\ \mathrm{K})$, separated at $n_\mathrm{H_2}\sim10^{3.8}\
\mathrm{cm}^{-3}$. NGC 253 has $\sim10$ times the high-density gas mass and
$\sim3$ times the dense-gas mass fraction of the GC. These properties are
consistent with their HCN/CO ratio but cannot alone explain the factor of
$\sim30$ difference in their star formation efficiencies (SFEs), contradicting
the dense-gas mass to star formation rate scaling law. The $n_\mathrm{H_2}$
histogram toward NGC 253 exhibits a shallow declining slope up to
$n_\mathrm{H_2}\sim10^6\ \mathrm{cm}^{-3}$, while that of the GC steeply drops
in $n_\mathrm{H_2}\gtrsim10^{4.5}\ \mathrm{cm}^{-3}$ and vanishes at $10^5\
\mathrm{cm}^{-3}$. Their dense-gas mass fraction ratio becomes consistent with
their SFEs when the threshold $n_\mathrm{H_2}$ for the dense gas is taken at
$\sim 10^{4.2\mbox{-}4.6}\ \mathrm{cm}^{-3}$. The rich abundance of gas above
this density range in the NGC 253 CMZ, or its scarcity in the GC, is likely to
be the critical difference characterizing the contrasting star formation in the
centers of the two galaxies.
