The structure and kinematics of the recognized stellar components of the Milky Way are explored, based on well-determined atmospheric parameters and kinematic quantities for 32360 “calibration stars” from the Sloan Digital Sky Survey (SDSS) and its first extension, (SDSS-II), which included the sub-survey SEGUE: Sloan Extension for Galactic Understanding and Exploration. Full space motions for a sub-sample of 16920 stars, exploring a local volume within 4 kpc of the Sun, are used to derive velocity ellipsoids for the inner- and outer-halo components of the Galaxy, as well as for the canonical thick-disk and proposed metal-weak thick-disk populations. This new sample of calibration stars represents an increase of 60% relative to the numbers used in a previous analysis. A Maximum Likelihood analysis of a local sub-sample of 16920 calibration stars has been developed in order to extract kinematic information for the major Galactic components (thick disk, inner halo, and outer halo), as well as for the elusive metal-weak thick disk (MWTD). We measure velocity ellipsoids for the thick disk, the MWTD, the inner halo, and the outer halo, demonstrate that the MWTD may be a component that is kinematically and chemically independent of the canonical thick disk (and put limits on the metallicity range of the MWTD), and derive the inferred spatial density profiles of the inner/outer halo components. We also present evidence for tilts in the velocity ellipsoids for stars in our sample as a function of height above the plane, for several ranges in metallicity, and confirm the shift of the observed metallicity distribution function (MDF) from the inner-halo to the outer-halo dominated sample.