  A nodeless $d$-wave state is likely in superconducting monolayer FeSe on
SrTiO$_3$. The lack of nodes is surprising but has been shown to be a natural
consequence of the observed small interband spin-orbit coupling. Here we
examine the evolution from a nodeless state to the nodal state as this
spin-orbit coupling is increased from a topological perspective. We show that
this evolution depends strongly on the orbital content of the superconducting
degrees of freedom. In particular, there are two $d$-wave solutions, which we
call orbitally trivial and orbitally nontrivial. In both cases, the nodes carry
a $\pm 2$ topological winding number that originates from a chiral symmetry.
However, the momentum space distribution of the positive and negative charges
is different for the two cases, resulting in a different evolution of these
nodes as they annihilate to form a nodeless superconductor. We further show
that the orbitally trivial and orbitally nontrivial nodal states exhibit
different Andreev flat band spectra at the edge.
