  We characterize ${\sim} 71,200$ W UMa type (EW) contact binaries, including
${\sim} 12,600$ new discoveries, using ASAS-SN $V$-band all-sky light curves
along with archival data from Gaia, 2MASS, AllWISE, LAMOST, GALAH, RAVE, and
APOGEE. There is a clean break in the EW period-luminosity relation at $\rm
\log (\rm P/d){\simeq}-0.30$, separating the longer period early-type EW
binaries from the shorter period, late-type systems. The two populations are
even more cleanly separated in the space of period and effective temperature,
by $\rm T_{eff}=6710\,K-1760\,K\,\log(P/0.5\,d)$. Early-type and late-type EW
binaries follow opposite trends in $\rm T_{eff}$ with orbital period. For
longer periods, early-type EW binaries are cooler, while late-type systems are
hotter. We derive period-luminosity relationships (PLRs) in the $W_{JK}$, $V$,
Gaia DR2 $G$, $J$, $H$, $K_s$ and $W_1$ bands for the late-type and early-type
EW binaries separated both by period and effective temperature, and by period
alone. The dichotomy of contact binaries is almost certainly related to the
Kraft break and the related changes in envelope structure, winds and angular
momentum loss.
