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Abstract 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_BB/L_X) between the UV/optical and X-ray, shows a wide range ofL_BB/L_X∈ (0.5, 3000) at early times and converges to disklike values ofL_BB/L_X∈ (0.5, 10) at late times. We estimate the fraction of optically discovered TDEs withL_X≥ 10⁴²erg s⁻¹to be at least 40% and show that X-ray loudness is independent of black hole mass. We argue that distinct disk formation timescales are unlikely to be able to explain the diverse range of X-ray evolution. We combine our sample with X-ray-discovered ones to construct an X-ray luminosity function, best fit by a broken power law, with a break atL_X≈ 10⁴⁴erg s⁻¹. We show that there is no dichotomy between optically and X-ray-selected TDEs; instead, there is a continuum of early-timeL_BB/L_X, at least as wide asL_BB/L_X∈ (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.