Magmatic iron meteorites are thought to sample the metallic cores of differentiated planetesimals and are subdivided into several chemical groups, each representing a distinct parent body. The only exceptions are the groups IIAB and IIG, which have been proposed to sample two immiscible melts from the same core. To test this model, we report the first Fe, Ni, O, and Cr isotope data for IIG iron meteorites and the first high-precision O isotope data for IIAB iron meteorites. The new data demonstrate that IIG iron meteorites belong to the non-carbonaceous (NC) meteorites. This is evident from the isotope anomaly of each of the four elements investigated, where the IIG irons always overlap with the compositions of NC meteorites but are distinct from those of carbonaceous (CC) meteorites. Moreover, among the NC meteorites and in particular, the NC irons, the isotopic composition of the IIG irons overlaps only with that of the IIAB irons. The combined Fe-Ni-O-Cr isotope data for IIAB and IIG iron meteorites, therefore, reveal formation from a single isotopic reservoir, indicating a strong genetic link between the two groups. The indistinguishable isotopic composition of the IIAB and IIG irons, combined with chemical evidence for the formation of IIG irons as late-stage liquids of the IIAB core, strongly suggests that both groups originate from the same core. The results underscore the strength of utilizing multiple elements and their isotopic compositions to establish genetic links among meteorites, rather than using a single element. They also highlight the significance of integrating multiple geochemical tracers and petrologic observations to accurately determine genetic relationships and the formation of meteorites within the same parent body.