The stellar surface density within the inner 1 kpc (Σ 1 ) has become a popular tool for understanding the growth of galaxies and its connection with the quenching of star formation. The emerging picture suggests that building a central dense core is a necessary condition for quenching. However, it is not clear whether changes in Σ 1 trace changes in stellar kinematics and the growth of dispersion-dominated bulges. In this paper, we combine imaging from the Sloan Digital Sky Survey with stellar kinematics from the Sydney-AAO Multi-object Integral-field unit (SAMI) and Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) surveys to quantify the correlation between Σ 1 and the proxy for stellar spin parameter within one effective radius (𝜆 𝑟 𝑒 ) for 1599 nearby galaxies. We show that, on the star-forming main sequence and at fixed stellar mass, changes in Σ 1 are mirrored by changes in 𝜆 𝑟 𝑒 . While forming stars, main sequence galaxies remain rotationally-dominated systems, with their Σ 1 increasing but their stellar spin staying either constant or slightly increasing. The picture changes below the main sequence, where Σ 1 and 𝜆 𝑟 𝑒 are no longer correlated. Passive systems show a narrower range of Σ 1 , but a wider range of 𝜆 𝑟 𝑒 compared to star-forming galaxies. Our results indicate that, from a structural point of view, passive galaxies are a more heterogeneous population than star-forming systems, and may have followed a variety of evolutionary paths. This also suggests that, if dispersion-dominated bulges still grow significantly at 𝑧 ∼0, this generally takes place during, or after, the quenching phase.