  To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based
superconductors, we performed comparative muon-spin rotation/relaxation
($\mu$SR) studies of superconducting noncentrosymmetric Re$_{0.82}$Nb$_{0.18}$
($T_c = 8.8$ K) and centrosymmetric Re ($T_c = 2.7$ K). In
Re$_{0.82}$Nb$_{0.18}$, the low temperature superfluid density and the
electronic specific heat evidence a fully-gapped superconducting state, whose
enhanced gap magnitude and specific-heat discontinuity suggest a moderately
strong electron-phonon coupling. In both Re$_{0.82}$Nb$_{0.18}$ and pure Re,
the spontaneous magnetic fields revealed by zero-field $\mu$SR below $T_c$
indicate time-reversal symmetry breaking and thus unconventional
superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and
noncentrosymmetric Re$T$ ($T$ = transition metal), yet its preservation in the
isostructural noncentrosymmetric superconductors Mg$_{10}$Ir$_{19}$B$_{16}$ and
Nb$_{0.5}$Os$_{0.5}$, strongly suggests that the local electronic structure of
Re is crucial for understanding the TRSB superconducting state in Re and Re$T$.
We discuss the superconducting order parameter symmetries that are compatible
with the observations.
