We study double gamma ($\gamma\gamma$) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation neutrinoless double-beta ($0\nu\beta\beta$) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in final $\beta\beta$ nuclei, particular $\gamma\gamma$ isobaric analog initial state into ground state. For with equal-e...