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-Zeldovich 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 $0.93pm0.03$, and the median ratio, $M_{500}^{rm SZ}/M_{500}^{rm X}= 0.91pm0.01$, is within the expectations from known X-ray calibration systematics. The $Y_{rm SZ}/Y_{rm X}$ ratio is $0.88pm0.02$, 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 ($0.89pm0.01$). 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.
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