The metallicity of local galaxies is tightly related not only to stellar mass, i.e. the mass-metallicity relation, but also to the star formation rate (SFR) through the so-called fundamental metallicity relation (FMR); more active galaxies show lower metallicities at fixed mass. Interestingly, high-z galaxies up to z ∼ 2.5 follow the same relation defined by SDSS locally. However, different shapes have been proposed for local galaxies, and the existence of a FMR and the role of the SFR has been recently questioned by some authors. In this paper we first discuss the various parametrizations of this mass-metallicity-SFR relation that has appeared in the literature to understand the origin of their different shapes. We then reanalysed data from CALIFA and SDSS-IV MaNGA surveys, which were used to suggest no dependency of metallicity on the SFR in local galaxies. Contrary to those claims, we find that those datasets are instead fully consistent with the predictions, showing the expected dependency on the SFR at fixed mass. Finally, we analysed those high-z data whose consistency with the local relation was questioned. While an internal dependency on the SFR among the subsamples is difficult to detect at high-z because of the limited dynamic range sampled in the three parameters and the intrinsic scatter and uncertainties of such small samples, all these datasets are compatible with the relation defined locally by SDSS galaxies. This confirms the lack of evolution of the FMR in these data up to z ∼ 2.3.