  Using angle-resolved photoemission spectroscopy, we show that the
recently-discovered surface state on SrTiO$_{3}$ consists of non-degenerate
$t_{2g}$ states with different dimensional characters. While the $d_{xy}$ bands
have quasi-2D dispersions with weak $k_{z}$ dependence, the lifted
$d_{xz}$/$d_{yz}$ bands show 3D dispersions that differ significantly from bulk
expectations and signal that electrons associated with those orbitals permeate
the near-surface region. Like their more 2D counterparts, the size and
character of the $d_{xz}$/$d_{yz}$ Fermi surface components are essentially the
same for different sample preparations. Irradiating SrTiO$_{3}$ in ultrahigh
vacuum is one method observed so far to induce the "universal" surface metallic
state. We reveal that during this process, changes in the oxygen valence band
spectral weight that coincide with the emergence of surface conductivity are
disproportionate to any change in the total intensity of the O $1s$ core level
spectrum. This signifies that the formation of the metallic surface goes beyond
a straightforward chemical doping scenario and occurs in conjunction with
profound changes in the initial states and/or spatial distribution of
near-$E_{F}$ electrons in the surface region.
