  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 study the effect of large-scale density field on scaling
relations. We present the identification of X-ray galaxy groups using a
combination of RASS and SDSS data. We include new X-ray reanalysis of RASS, to
include very extended (up to a size of half a degree) sources and account for
differences in the limiting sensitivity towards compact and very extended X-ray
emission. 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 the primary candidates for being the contaminants in the optical
group catalogues. Removing those groups from the optical group sample using
optically measured properties only, leads to a substantial reduction in the
scatter in the most scaling relations of the optical groups. We find a density
dependence of both the X-ray and optical luminosity of groups, which we
associate with the assembly bias. Abridged.
