  There have been increasing efforts in realizing topological metallic phases
with nontrivial surface states. It was suggested that orthorhombic perovskite
iridates are classified as a topological crystalline metal (TCM) with flat
surface states protected by lattice symmetries. Here we perform
first-principles electronic structure calculations for epitaxially stabilized
orthorhombic perovskite iridates. Remarkably, two different types of
topological surface states are found depending on surface directions. On side
surfaces, flat surface states protected by lattice symmetries emerge,
manifesting the topological crystalline character. On the top surface, on the
other hand, an unexpected Dirac cone appears, indicating surface states
protected by a time-reversal symmetry, which is confirmed by the presence of a
nontrivial topological $\mathbb{Z}_2$ index. These results suggest that the
orthorhombic iridates are unique systems exhibiting both lattice- and
global-symmetry-protected topological phases and surface states. Transitions to
weak and strong topological insulators and implications of surface states in
light of angle resolved photoemission spectroscopy are also discussed.
