We combine the latest observations of disc galaxy photometry and rotation curves at moderate redshift from the FORS Deep Field (FDF) with simple models of chemical enrichment. Our method describes the build‐up of the stellar component through infall of gas and allows for gas and metal outflows. In this framework, we keep a minimum number of constraints and we search a large volume of parameter space, looking for the models that best reproduce the photometric observations in the observed redshift range (0.5 < z < 1). We find that star formation efficiency correlates well with vmax, so that massive discs are more efficient in the formation of stars and have a smaller spread in stellar ages. This trend presents a break at around vmax∼ 140 km s−1. Galaxies on either side of this threshold have significantly different age distributions. This break has been already suggested by several authors in connection with the contribution from either gravitational instabilities or supernova‐driven turbulence to star formation. The gas infall time‐scale and gas outflows also present a correlation with galaxy mass, so that massive discs have shorter infall time‐scales and smaller outflow fractions. The model presented in this paper suggests that massive discs have formation histories resembling those of early‐type galaxies, with highly efficient and short‐lived bursts, in contrast with low‐mass discs, which have a more extended star formation history. The ages correlate well with galaxy mass or luminosity, and the predicted gas‐phase metallicities are consistent with the observations of local and moderate‐redshift galaxies. One option to explain the observed shallow slope of the Tully-Fisher relation at intermediate redshift could be small episodes of star formation in low‐mass disc