The stellar mass Tully-Fisher relation (STFR) and its scatter encode valuable information about the processes shaping galaxy evolution across cosmic time. However, we are still missing a proper quantification of the STFR slope and scatter dependence on the baryonic tracer used to quantify rotational velocity, on the velocity measurement radius and on galaxy integrated properties. We present a catalogue of stellar and ionized gas (traced by H{alpha} emission) kinematic measurements for a sample of galaxies drawn from the MaNGA Galaxy Survey, providing an ideal tool for galaxy formation model calibration and for comparison with high-redshift studies. We compute the STFRs for stellar and gas rotation at 1, 1.3 and 2 effective radii (Re). The relations for both baryonic components become shallower at 2Re compared to 1Re and 1.3Re. We report a steeper STFR for the stars in the inner parts (<=1.3Re) compared to the gas. At 2Re, the relations for the two components are consistent. When accounting for covariances with integrated v/{sigma}, scatter in the stellar and gas STFRs shows no strong correlation with: optical morphology, star formation rate surface density, tidal interaction strength or gas accretion signatures. Our results suggest that the STFR scatter is driven by an increase in stellar/gas dispersional support, from either external (mergers) or internal (feedback) processes. No correlation between STFR scatter and environment is found. Nearby Universe galaxies have their stars and gas in statistically different states of dynamical equilibrium in the inner parts (<=1.3Re), while at 2Re the two components are dynamically coupled.