We analysed a sample of 552 galaxies from the LEGA-C spectroscopic survey (0.6<z<0.77), for which we estimated the stellar population parameters by a Bayesian analysis of the stellar absorption features and photometry. We investigated the effect of the current star formation activity on light-weighted mean stellar ages and metallicities and their median trends with stellar mass or velocity dispersion. The bimodality in the global age-mass relation stems from the different age distributions in the quiescent and star-forming populations. No bimodality is observed in the stellar metallicity-mass relation, although quiescent and star-forming galaxies have different distributions in this parameter space. We identified a high-metallicity sequence populated by quiescent and weakly star-forming galaxies. At masses lower than 10^10.8^M_{sun}_, the median stellar metallicity-mass relation of star-forming galaxies steepens as a consequence of the increasing scatter towards lower stellar metallicities for galaxies with an increasing specific star formation rate at fixed mass. Relying on a consistent analysis of SDSS DR7 spectra and accounting for aperture corrections, we quantified the evolution of the volume-weighted stellar age and stellar metallicity scaling relations between z=0.7 and the present. We found negligible evolution in the stellar metallicity-mass relation of quiescent galaxies and for M*>10^11^M_{sun}_ galaxies in general. Lower-mass star-forming galaxies instead have typically lower metallicities than their local counterparts, indicating significant enrichment since z~0.7 in the low-mass regime. Notably, the median of the stellar ages of the general population and of quiescent galaxies has changed by only 2Gyr between z=0.7 and z=0.1, which is less than expected from cosmic ageing. Some quiescent galaxies must evolve passively to reach the old boundary of the local population. In order to explain the evolution of the median trends, however, both individual evolution through rejuvenation and/or minor merging that affects the outer galaxy regions and population evolution through quenching of massive metal-rich star-forming galaxies are required.