(Abridged) Context: Both X-ray and radio observations offer insight into the high-energy processes of young stellar objects (YSOs). The observed thermal X-ray emission can be accompanied by both thermal and nonthermal radio emission. Due to variability, simultaneous X-ray and radio observations are a priori required, but results have been inconclusive. Aims: We use archival X-ray and radio observations of the Orion Nebula Cluster (ONC) to significantly enlarge the sample size of known YSOs with both X-ray and radio detections. Methods: We study the ONC using multi-epoch non-simultaneous archival Chandra X-ray and NRAO Very Large Array (VLA) single-band radio data. The multiple epochs allow us to reduce the impact of variability by obtaining approximated quiescent fluxes. Results: We find that only a small fraction of the X-ray sources (7%) have radio counterparts, even if 60% of the radio sources have X-ray counterparts. The radio flux density is typically too low to distinguish thermal and nonthermal radio sources. Only a small fraction of the YSOs with detections in both bands are compatible with the empirical Guedel-Benz (GB) relation. Most of the sources not compatible with the GB relation are proplyds, and thus likely thermal sources, but only a fraction of the proplyds is detected in both bands, such that the role of these sources is inconclusive. Conclusions: While the radio sources appear to be globally unrelated to the X-ray sources, the X-ray dataset clearly is much more sensitive than the radio data. We find tentative evidence that known non-thermal radio sources and saturated X-ray sources are indeed close to the empirical relation, even if skewed to higher radio luminosities, as they are expected to be. Most of the sources that are clearly incompatible with the empirical relation are proplyds which could instead plausibly be thermal radio sources.
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