Comparative analyses of the nuclear matrix elements (NMEs) related to the 0νβ+β+ decay of 106Cd to the ground state of 106Pd and the ordinary muon capture (OMC) in 106Cd are performed. This is the first time the OMC NMEs are studied for a nucleus decaying via positron-emitting/electron-capture modes of double beta decay. All the present calculations are based on the proton-neutron quasiparticle random-phase approximation with large no-core single-particle bases and realistic two-nucleon interactions. The effect of the particle-particle interaction parameter gpp of pnQRPA on the NMEs is discussed. In the case of the OMC, the effect of different bound-muon wave functions is studied.