We study the link between the kinematic-morphology of galaxies, as inferred from integral-field stellar kinematics, and their relation between mass and star formation rate (SFR). Our sample consists of $sim 3200$ galaxies with integral-field spectroscopic data from the MaNGA survey with available determinations of their effective stellar angular momentum within the half-light radius $lambda_{R_e}$. We find that for star-forming galaxies, namely along the star formation main sequence (SFMS), the $lambda_{R_e}$ values remain large and almost unchanged over about two orders of magnitude in stellar mass, with the exception of the lowest masses $mathcal{M}_{star}lesssim2times10^{9} mathcal{M}_{odot}$, where $lambda_{R_e}$ slightly decreases. The SFMS is dominated by spiral galaxies with small bulges. Below the SFMS, but above the characteristic stellar mass $mathcal{M}_{rm crit}approx2times10^{11} mathcal{M}_{odot}$, there is a sharp decrease in $lambda_{R_e}$ with decreasing star formation rate: massive galaxies well below the SFMS are mainly slow-rotator early-type galaxies, namely genuinely spheroidal galaxies without disks. Below the SFMS and below $mathcal{M}_{rm crit}$ the decrease of $lambda_{R_e}$ with decreasing SFR becomes modest or nearly absent: low-mass galaxies well below the SFMS, are fast-rotator early-type galaxies, and contain fast-rotating stellar disks like their star-forming counterparts. We also find a small but clear environmental dependence for the massive galaxies: in the mass range $10^{10.9}-10^{11.5} mathcal{M}_{odot}$, galaxies in rich groups or denser regions or classified as central galaxies have lower values of $lambda_{R_e}$. While no environmental dependence is found for galaxies of lower mass. We discuss how our results can be understood as due to the different star formation and mass assembly histories of galaxies with varying mass.
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