In my talk I discuss on what is currently known on the theoretical interpretation of the top-quark mass parameter in Monte-Carlo event generators (MCs), as measured in the direct top-mass measurements. The interpretation is associated to the perturbative part of the MCs, namely the parton shower, as well as on the way howthe infrared evolution of the parton shower is terminated through thecutoff parameter. Nevertheless, also the hadronization modelplays an important role. This implies that, in order to solve the top-mass interpretation problem, the shower cutoff should be treated like a factorization scale and not like a tuned parameter. I explain the conceptual and practical implications of this rather novel view, and its interplay with the top-mass calibration method, which I have developed some time ago.