We present the homogeneous abundance analysis for a combined sample of 185 giants in the bulge globular cluster (GC) NGC 6388. Our results are used to describe the multiple stellar populations and differences or analogies with bulge field stars. Proton-capture elements indicate that a single class of first-generation polluters is sufficient to reproduce both the extreme and intermediate parts of the anti-correlations among light elements O, Na, Mg, and Al, which is at odds with our previous results based on a much smaller sample. The abundance pattern of other species in NGC 6388 closely tracks the trends observed in bulge field stars. In particular, the α-elements, including Si, rule out an accreted origin for NGC 6388, confirming our previous results based on iron-peak elements, chemo-dynamical analysis, and the age-metallicity relation. The neutron-capture elements are generally uniform, although the [Zr/Fe] ratio shows an intrinsic scatter, correlated to Na and Al abundances. Instead, we do not find enhancement in neutron-capture elements for stars whose photometric properties would classify NGC 6388 as a type II GC. Together with the homogeneity in [Fe/H] we found in a previous paper, this indicates we need to better understand the criteria to separate classes of GCs, coupling photometry, and spectroscopy. These results are based on abundances of 22 species (O, Na, Mg, Al, Si, Ca, Ti, Sc, V, Cr, Mn, Fe, Co, Ni, Zn, Y, Zr, Ba, La, Ce, Nd, and Eu) from UVES spectra sampling proton-, α-, neutron-capture elements, and Fe-peak elements. For 12 species, we also obtain abundances in a large number of giants (up to 150) from GIRAFFE spectra.