  We show that a pair of overlapping Majorana bound states (MBSs) forming a
partially-separated Andreev bound state (ps-ABS) represents a generic
low-energy feature in spin-orbit coupled semiconductor-superconductor (SM-SC)
hybrid nanowires in the presence of a Zeeman field. In a finite nanowire the
ps-ABS interpolates continuously between the "garden variety" ABS, which
consists of two MBSs sitting on top of each other, and the topologically
protected Majorana zero modes (MZMs), which are separated by a distance given
by the length of the wire. Despite being topologically trivial, ps-ABSs can
generate signatures identical to MZMs in local charge tunneling experiments. In
particular, the height of the zero bias conductance peak (ZBCP) generated by
ps-ABSs has the quantized value, 2e2/h, and it can remain unchanged in an
extended range of experimental parameters, such as Zeeman field and the tunnel
barrier height. We illustrate the formation of such low-energy robust ps-ABSs
in two experimentally relevant situations: a hybrid SM-SC system consisting of
a proximitized nanowire coupled to a quantum dot and the SM-SC system in the
presence of a spatially varying inhomogeneous potential. We then show that,
unlike local measurements, a two-terminal experiment involving charge tunneling
at both ends of the wire is capable of distinguishing the non-Abelian MZMs from
the generic ps-ABSs. While the MZMs localized at the opposite ends of the wire
generate correlated differential conduction spectra, including correlations in
energy splittings and critical Zeeman fields associated with the emergence of
the ZBCPs, such correlations are absent if the ZBCPs are due to ps-ABSs
emerging in the topologically trivial phase. Measuring such correlations is the
clearest and most straightforward test of topological MZMs in SM-SC
heterostructures that can be done in a currently accessible experimental
set-up.
