  Molecular systems can exhibit a complex, chemically tailorable inner
structure which allows for targeting of specific mechanical, electronic and
optical properties. At the single-molecule level, two major complementary ways
to explore these properties are molecular quantum-dot structures and scanning
probes. This article outlines comprehensive principles of electron-transport
spectroscopy relevant to both these approaches and presents a new,
high-resolution experiment on a high-spin single-molecule junction exemplifying
these principles. Such spectroscopy plays a key role in further advancing our
understanding of molecular and atomic systems, in particular the relaxation of
their spin. In this joint experimental and theoretical analysis, particular
focus is put on the crossover between resonant regime [single-electron
tunneling (SET)] and the off-resonant regime [inelastic electron (co)tunneling
(IETS)]. We show that the interplay of these two processes leads to unexpected
mirages of resonances not captured by either of the two pictures alone.
Although this turns out to be important in a large fraction of the possible
regimes of level positions and bias voltages, it has been given little
attention in molecular transport studies. Combined with nonequilibrium IETS --
four-electron pump-probe excitations -- these mirages provide crucial
information on the relaxation of spin excitations. Our encompassing physical
picture is supported by a master-equation approach that goes beyond weak
coupling. The present work encourages the development of a broader connection
between the fields of molecular quantum-dot and scanning probe spectroscopy.
