  Using Chandra observations, we derive the $Y_{\rm X}$ proxy and associated
total mass measurement, $M_{500}^{\rm Y_X}$, for 147 clusters with $z \leq
0.35$ from the Planck Early Sunyaev-Zel'dovich catalog, and for 80 clusters
with $z \leq 0.30$ from an X-ray flux-limited sample. We re-extract the Planck
$Y_{\rm SZ}$ measurements and obtain the corresponding mass proxy,
$M_{500}^{\rm SZ}$, from the full Planck mission maps, minimizing the Malmquist
bias due to observational scatter. The masses re-extracted using the more
precise X-ray position and characteristic size agree with the published PSZ2
values, but yield a significant reduction in the scatter (by a factor of two)
in the $M_{500}^{\rm SZ}$-$M_{500}^{\rm X}$ relation. The slope is
$0.93\pm0.03$, and the median ratio, $M_{500}^{\rm SZ}/M_{500}^{\rm X}=
0.91\pm0.01$, is within the expectations from known X-ray calibration
systematics. The $Y_{\rm SZ}/Y_{\rm X}$ ratio is $0.88\pm0.02$, in good
agreement with predictions from cluster structure, and implying a low level of
clumpiness. In agreement with the findings of the Planck Collaboration, the
slope of the $Y_{\rm SZ}$-$D_{\rm A}^{-2} Y_{X}$ flux relation is significantly
less than unity ($0.89\pm0.01$). Using extensive simulations, we show that this
result is not due to selection effects, intrinsic scatter, or covariance
between quantities. We demonstrate analytically that changing the $Y_{\rm
SZ}$-$Y_{X}$ relation from apparent flux to intrinsic properties results in a
best-fit slope that is closer to unity and increases the dispersion about the
relation. The redistribution resulting from this transformation implies that
the best fit parameters of the $M_{500}^{\rm SZ}$-$M_{500}^{\rm X}$ relation
will be sample-dependent.
