The stellar population of a galaxy contains a record of its star formation and assembly history, making it an important area of research to develop our understanding of galaxy formation and evolution. We present two works, the first focusing on early-type galaxies (ETGs), the second on star-forming galaxies (SFGs). These works aim to understand the link between the overall structure and dynamics of a galaxy, and the evolution of the stars within it. Our samples are comprised of 625 ETGs with integral-field spectroscopy, and a sample of 3226 SFGs using single-fibre spectra from the Sloan Digital Sky Survey with the technique of aperture-matched sampling. Currently, the well-established correlations between the mass of a galaxy and the properties of its stars are considered evidence for mass driving the evolution of the stellar population. However, for both ETGs and SFGs, compared to correlations with mass, the [Z/H]—gravitational potential and age—surface density relations show both smaller scatter and less residual trend with galaxy size. We interpret these results as evidence that the gravitational potential is the primary regulator of global stellar metallicity, via its relation to the gas escape velocity. Furthermore, we propose two possible mechanisms for the age— surface density relation: (a) the age–surface density correlation arises as results of compactness-driven quenching mechanisms; and/or (b) as a fossil record of the star formation rate density—gas density relation in their disk-dominated progenitors.