  The surface and bulk states in topological materials have shown promise in
many applications. Grey or $\alpha$-Sn, the inversion symmetric analogue to
HgTe, can exhibit a variety of these phases. However there is disagreement in
both calculation and experiment over the exact shape of the bulk bands and the
number and origin of the surface states. Using spin- and angle-resolved
photoemission we investigate the bulk and surface electronic structure of
$\alpha$-Sn thin films on InSb(001) grown by molecular beam epitaxy. We find
that there is no significant warping in the shapes of the bulk bands. We also
observe the presence of only two surface states near the valence band maximum
in both thin (13 bilayer) and thick (400 bilayer) films. In 50 bilayer films,
these two surface states coexist with quantum well states. Surprisingly, both
of these surface states are spin-polarized with orthogonal spin-momentum
locking and opposite helicities. One of these states is the spin-polarized
topological surface state and the other a spin resonance. Finally, the presence
of another orthogonal spin-momentum locked topological surface state from a
secondary band inversion is verified. Our work clarifies the electronic
structure of $\alpha$-Sn(001) such that better control of the electronic
properties can be achieved. In addition, the presence of two spin-polarized
surface states near the valence band maximum has important ramifications for
the use of $\alpha$-Sn in spintronics.
