We present the metallicity results from the ARGOS spectroscopic survey of the Galactic bulge. Our aim is to understand the formation of the Galactic bulge: did it form via mergers, as expected from Λ cold dark matter theory, or from disc instabilities, as suggested by its boxy/peanut shape, or both? Our stars are mostly red clump giants, which have a well-defined absolute magnitude from which distances can be determined. We have obtained spectra for 28 000 stars at a spectral resolution of R = 11 000. From these spectra, we have determined stellar parameters and distances to an accuracy of <1.5 kpc. The stars in the inner Galaxy span a large range in Fe/H, −2.8 ≤ Fe/H ≤ +0.6. From the spatial distribution of the red clump stars as a function of Fe/H, we propose that the stars with Fe/H > −0.5 are part of the boxy/peanut bar/bulge. We associate the lower metallicity stars (Fe/H < −0.5) with the thick disc, which may be puffed up in the inner region, and with the inner regions of the metal-weak thick disc and inner halo. For the bulge stars with Fe/H > −0.5, we find two discrete populations: (i) stars with Fe/H −0.25 which provide a roughly constant fraction of the stars in the latitude interval b = −5° to −10°, and (ii) a kinematically colder, more metal-rich population with mean Fe/H +0.15 which is more prominent closer to the plane. The changing ratio of these components with latitude appears as a vertical abundance gradient of the bulge. We attribute both of these bulge components to instability-driven bar/bulge formation from the thin disc. We associate the thicker component with the stars of the early less metal-rich thin disc, and associate the more metal-rich population concentrated to the plane with the colder more metal-rich stars of the early thin disc, similar to the colder and younger more metal-rich stars seen in the thin disc in the solar neighbourhood today. We do not exclude a weak underlying classical merger-generated bulge component, but see no obvious kinematic association of any of our bulge stars with such a classical bulge component. The clear spatial and kinematic separation of the two bulge populations (i) and (ii) makes it unlikely that any significant merger event could have affected the inner regions of the Galaxy since the time when the bulge-forming instabilities occurred.