Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE$_{1-delta}$Sr$_delta$NiO$_2$ (RE$=$Nd, Pr), we study the role of Hunds coupling $J$ in a quarter-filled two-orbital Hubbard model which has been on the periphery of the attention. A region of negative effective Coulomb interaction of this model is revealed to be differentiated from three- and five-orbital models in their typical Hunds metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator while the other three, which we call intermediate metal, weak Hunds metal, and valence-skipping metal, from the effect of $J$ being away from Mottness. Defining criteria characterizing these metals are suggested, establishing the existence of Hunds metallicity in two-orbital systems.
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