Exploring the Diversity of Groups at 0.1<z<0.8 with X-ray and Optically
  Selected Samples
  We present the global group properties of two samples of galaxy groups
containing 39 high quality X-ray selected systems and 38 optically
(spectroscopically) selected systems in coincident spatial regions at
0.12<z<0.79. Only nine optical systems are associable with X-ray systems. We
discuss the confusion inherent in the matching of both galaxies to extended
X-ray emission and of X-ray emission to already identified optical systems.
Extensive spectroscopy has been obtained and the resultant redshift catalog and
group membership are provided here. X-ray, dynamical, and total stellar masses
of the groups are also derived and presented. We explore the effects of
applying three different kinds of radial cut to our systems: a constant cut of
1 Mpc and two r200 cuts, one based on the velocity dispersion of the system and
the other on the X-ray emission. We find that an X-ray based r200 results in
less scatter in scaling relations and less dynamical complexity as evidenced by
results of the Anderson-Darling and Dressler-Schectman tests, indicating that
this radius tends to isolate the virialized part of the system. The constant
and velocity dispersion based cuts can overestimate membership and can work to
inflate velocity dispersion and dynamical and stellar mass. We find Lx-sigma
and Mstellar-Lx scaling relations for X-ray and optically selected systems are
not dissimilar. The mean fraction of mass found in stars for our systems is
approximately 0.014 with a logarithmic standard deviation of 0.398 dex. We also
define and investigate a sample of groups which are X-ray underluminous given
the total group stellar mass. For these systems the fraction of stellar mass
contributed by the most massive galaxy is typically lower than that found for
the total population of groups implying that there may be less IGM contributed
from the most massive member in these systems. (Abridged)
