  We use 3653 (2661 RRab, 992 RRc) RR Lyrae stars (RRLs) with 7D (3D position,
3D velocity, and metallicity) information selected from SDSS, LAMOST, and Gaia
EDR3, and divide the sample into two Oosterhoff groups (Oo I and Oo II)
according to their amplitude-period behaviour in the Bailey Diagram. We present
a comparative study of these two groups based on chemistry, kinematics, and
dynamics. We find that Oo I RRLs are relatively more metal rich, with
predominately radially dominated orbits and large eccentricities, while Oo II
RRLs are relatively more metal poor, and have mildly radially dominated orbits.
The Oosterhoff dichotomy of the Milky Way's halo is more apparent for the
inner-halo region than for the outer-halo region. Additionally, we also search
for this phenomenon in the halos of the two largest satellite galaxies, the
Large and Small Magellanic clouds (LMC, SMC), and compare over different bins
in metallicity. We find that the Oosterhoff dichotomy is not immutable, and
varies based on position in the Galaxy and from galaxy-to-galaxy. We conclude
that the Oosterhoff dichotomy is the result of a combination of stellar and
galactic evolution, and that it is much more complex than the dichotomy
originally identified in Galactic globular clusters.
