Context. Advances in cosmological studies require us to improve our understanding of the baryonic content of galaxy groups. The key baryonic components of groups are galaxies and hot gas, while key non-baryonic mass tracers are the velocity dispersion of galaxies and the distribution of galaxies within the group.

Aims. We revisit the picture of X-ray emission of groups through the study of systematic differences in the optical properties of groups, with and without X-ray emission, and we study the effect of the large-scale density field on scaling relations.

Methods. We present the identification of X-ray galaxy groups using a combination of ROSAT All Sky Survey (RASS) and Sloan Digital Sky Survey (SDSS) data. We include a new X-ray reanalysis of RASS, covering very extended (up to a size of half a degree) sources, and we account for differences in the limiting sensitivity with respect to compact and very extended X-ray emission. We applied a screening of the identified X-ray sources, based on the optical properties, to achieve 95% clean catalogues. We used a mock SDSS survey to understand the performance of our FoF group finder and applied the CLEAN algorithm to revise group mass estimates and achieve a clean membership catalogue.

Results. X-ray groups exhibit less scatter in the scaling relations and selecting the groups based on the extended X-ray emission leads to an additional scatter reduction. Most of the scatter for the optical groups is associated with a small (6%) fraction of outliers, primarily associated with low optical-luminosity groups found in dense regions of the cosmic web. These groups are primary candidates for the contaminants in the optical group catalogues. We find that removing only those groups from the optical group sample using optically measured properties leads to a substantial reduction in the scatter of the scaling relations of the optical groups. We report a dependence of both the X-ray and optical luminosity of groups on large-scale density, which we associate with the assembly bias. These results motivate an introduction of an additional characterization of galaxy clusters and shed light on the physical origin of anomalous clustering of galaxy clusters, found by the Dark Energy Survey (DES).