Iron oxide-copper-gold (IOCG) and iron oxide-apatite (IOA) deposits are commonly spatially and temporally associated with one another, and with coeval magmatism. IOCG deposits have similar Cu grades and tonnages as porphyry-Cu deposits but are distinguished by having significantly less total sulfur and lacking stockwork quartz veins. In many districts, field observations reveal that IOCG mineralization transitions with depth to S-Cu-Au-poor IOA mineralization, and/or that IOA mineralization transitions laterally to IOCG mineralization. Here, we use trace element concentrations in magnetite and pyrite, Fe and O stable isotope abundances of magnetite and hematite, H isotopes of magnetite-hosted fluid inclusions and actinolite, and S in pyrite from IOCG and IOA deposits in Chile and Peru to develop a new genetic model that explains IOCG and IOA deposits as a continuum produced by a combination of igneous and magmatic-hydrothermal processes. The δ¹⁸O, Δ¹⁷O, δ⁵⁶Fe, δD and δ³⁴S data unequivocally fingerprint a silicate magma as the source of the ore fluid in Andean IOCG and IOA deposits. Magnetite-hosted silicate melt inclusions and aqueous fluid inclusions, along with magnetite trace element compositions, reveal crystallization from silicate melt and magmatic-hydrothermal fluid. The trace element abundances of magnetite and pyrite, and Mg-in-magnetite and Fe# actinolite thermometry, reveal a systematic continuum between IOA and IOCG deposits that is consistent with formation from a cooling magmatic-hydrothermal fluid. The compositional variability of actinolite in IOCG systems indicates that at least two separate magmatic-hydrothermal fluids were involved in mineralization. The first fluid was responsible for the massive and disseminated magnetite, actinolite and Cu-poor sulfides, whereas the second fluid precipitated additional magnetite and actinolite along with Cu-Fe-sulfides. The data are consistent with a model that invokes a magmatic-hydrothermal ore fluid that evolves an intermediate to intermediate-mafic silicate melt and ascends along pre-existing faults into the ore deposition environment owing to regional tectonic stress changes.