Depending on whether a T Tauri star accretes material from its circumstellar disk or not, different X-ray emission properties can be found. The accretion shocks produce cool heating of the plasma, contributing to the soft X-ray emission from the star. Using X-ray data from the Chandra Orion Ultra-deep Project and accretion rates that were obtained with the Hubble Space Telescope/WFPC2 photometric measurements in the Orion Nebula Cluster, we studied the relation between the accretion processes and the X-ray emissions of a coherent sample of T Tauri sources in the region. We performed regression and correlation analyses of our sample of T Tauri stars between the X-ray parameters, stellar properties, and the accretion measurements. We find that a clear anti-correlation is present between the residual X-ray luminosity and the accretion rates in our samples in Orion that is consistent with that found on the XMM-Newton Extended Survey of the Taurus molecular cloud (XEST) study. We provide a catalog with X-ray luminosities (corrected from distance) and accretion measurements of an Orion Nebula Cluster (ONC) T Tauri stars sample. Although Orion and Taurus display strong differences in their properties (total gas and dust mass, star density, strong irradiation from massive stars), we find that a similar relation between the residual X-ray emission and accretion rate is present in the Taurus molecular cloud and in the accreting samples from the Orion Nebula Cluster. The spread in the data suggests dependencies of the accretion rates and the X-ray luminosities other than the stellar mass, but the similarity between Orion and Taurus hints at the environment not being one of them. The anti-correlation between the residual X-ray luminosity and mass accretion rate is inherent to the T Tauri stars in general, independent of their birthplace and environment, and intrinsic to early stellar evolution.

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