We revisit the picture of X-ray emission of groups, taking into account possible off-centering in the group position as well as differences in the X-ray appearance of groups. We study systematic differences in the optical properties of groups with and without X-ray emission, taking into account X-ray completeness and mass-driven trends. We present 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 (upto a size of half a degree) sources, and account for differences in the limiting sensitivity towards compact and very extended X-ray emission. We apply a screening of the identified X-ray sources, based on the optical properties, to achieve 95% clean catalogs. We use mock of SDSS survey to understand the performance of our FoF group finder and apply Clean algorithm to revise group mass estimates and achieve a clean membership catalog. Catalogs produced in this work are available online. We tabulate the scaling relations of X-ray and optical properties of groups. We find that subclass of extended-only X-ray groups is very close in its properties to non-X-ray groups, except for not covering part of non-X-ray groups having large crossing times. Among the confirmed trends for X-ray groups is a similarly large scatter in M/L ratio, compared to optical groups, which previously was considered the main difference between the two populations. Remaining differences in the groups suggest selecting higher overdensities for cosmological studies using X-ray group mass function.