Probing the dichotomy between Yu-Shiba-Rusinov and Majorana bound states via conductance, quantum noise and $\Delta_T$ noise

We investigate charge and spin conductance, charge and spin quantum noise, along with charge and spin $\Delta_T$ noise, as diagnostic tools to distinguish Yu-Shiba-Rusinov (YSR) states from Majorana-bound states (MBS) in a one-dimensional metal/spin-flipper/metal/insulator/superconductor junction. YSR states arise from magnetic impurities acting as spin-flippers within a trivial s-wave superconducting gap, while MBS emerge in topological superconductors, often leading to ambiguity in experiments where magnetic impurities mimic zero-energy MBS signatures. By replacing the trivial superconductor with a topological one exhibiting triplet pairing (e.g., chiral p or spinless p-wave nanowires), we identify robust and distinguishing features of YSR and MBS states. Our analysis demonstrates that combined measurements of both charge and spin conductance, charge and spin quantum noise, and their $\Delta_T$ noise counterparts offer unique and reliable signatures to differentiate YSR states from genuine MBS, thereby reducing false-positive interpretations in topological superconductivity experiments.