  We investigate the role of the Bloch functions and superconducting gap
symmetries on the formation and properties of impurity-induced resonances in a
two-dimensional superconductor, and elucidate their manifestation in scanning
tunneling spectra. We use and extend a recently developed scattering approach,
conveniently formulating the results in terms of the phase shifts of electron
scattering off the impurity. We find that the discrete subgap states in a
nodeless-gap superconductor are insensitive to the potential scattering phase
shift (common for the two spin species) if time-reversal symmetry (TRS) is
preserved. The independence of potential scattering is exact for $s$-wave
superconductors. It remains an accurate approximation over a broad range of
subgap energies when the gap function breaks the lattice point symmetry, except
for a narrow region below the gap edge. Breaking of TRS makes potential
scattering capable of creating spin-degenerate subgap states, which may be
further split by spin-dependent scattering. In nodal-gap superconductors,
impurity-induced resonances are broadened by coupling to the quasiparticle
continuum. We identify the conditions allowing for the formation of narrow
resonances. In addition to finding the energy spectrum, we evaluate the
spin-resolved differential conductance for all of the considered symmetries and
gap structures.
