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 the resonant regime [single-electron tunneling] and the off-resonant regime [inelastic electron (co)tunneling spectroscopy (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.