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We explore local and global dynamical differences between the kinematics of ionised gas and stars in a sample of galaxies from Data Release 3 of the SAMI Galaxy Survey. We find better agreement between local (i.e., comparing on a spaxel-to-spaxel basis) velocities and dispersion of gas and stars in younger systems as with previous work on the asymmetric drift in galaxies, suggesting that the dynamics of stars and ionised gas are initially coupled. The intrinsic scatter around the velocity and dispersion relations increases with increasing stellar age and mass, suggesting that subsequent mechanisms such as internal processes, divergent star formation and assembly histories also play a role in setting and altering the dynamics of galaxies. The global (flux-weighted) dynamical support of older galaxies is hotter than in younger systems. We find that the ionised gas in galaxies is almost always dynamically colder than the stars with a steeper velocity gradient. In absolute terms, the local difference in velocity dispersion is more pronounced than the local difference in velocity, possibly reflecting inherent differences in the impact of turbulence, inflow and/or feedback on gas compared to stars. We suggest how these findings may be taken into account when comparing high and low redshift galaxy samples to infer dynamical evolution., Comment: 11 pages, 9 figures, 1 table, accepted for publication in MNRAS