  We present a systematic analysis of the X-ray emission of a sample of 17
optically selected, X-ray-detected tidal disruption events (TDEs) discovered
between 2014 and 2021. The X-ray light curves show a diverse range of temporal
behaviors, with most sources not following the expected power-law decline. The
X-ray spectra are mostly extremely soft and consistent with thermal emission
from the innermost region of an accretion disk, which cools as the accretion
rate decreases. Three sources show formation of a hard X-ray corona, at
late-times. The spectral energy distribution shape, probed by the ratio
($L_{\rm\,BB}/L_{\rm\,X}$) between the UV/optical and X-ray, shows a wide range
$L_{\rm BB}/L_{\rm X}\,\in\,(0.5,\,3000)$ at early-times, and converges to
disk-like values $L_{\rm\,BB}/L_{\rm\,X}\,\in\,(0.5,\,10)$ at late-times. We
estimate the fraction of optically discovered TDEs with $L_{\rm\,X}\,\geq
10^{42}~\rm{erg}~\rm{s}^{-1} $ to be at least $40\%$, and show that X-ray
loudness is independent of black hole mass. We argue that distinct disk
formation time scales are unlikely to fully explain the diverse range of X-ray
evolutions. We combine our sample with X-ray discovered ones to construct an
X-ray luminosity function, best fitted by a broken power-law, with a break at
$L_{\rm\,X} \approx 10^{44}~\rm{erg}~\rm{s}^{-1} $. We show that there is no
dichotomy between optically and X-ray selected TDEs, instead there is a
continuum of early time $L_{\rm\,BB}/L_{\rm\,X}$, at least as wide as
$L_{\rm\,BB}/L_{\rm\,X}\,\in\,(0.1,\,3000)$, with optical/X-ray surveys
selecting preferentially, but not exclusively, from the higher/lower end of the
distribution. Our findings are consistent with unification models for the
overall TDE population.
