We investigate a sample of 40 local, main-sequence, edge-on disc galaxies using integral field spectroscopy with the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey to understand the link between properties of the extraplanar gas and their host galaxies. The kinematics properties of the extraplanar gas, including velocity asymmetries and increased dispersion, are used to differentiate galaxies hosting large-scale galactic winds from those dominated by the extended diffuse ionized gas. We find rather that a spectrum of diffuse gas-dominated to wind-dominated galaxies exist. The wind-dominated galaxies span a wide range of star formation rates (SFRs; -1 ≲ log (SFR/M⊙ yr-1) ≲ 0.5) across the whole stellar mass range of the sample (8.5 ≲ log (M*/M⊙) ≲ 11). The wind galaxies also span a wide range in SFR surface densities (10-3-10-1.5M⊙ yr-1 kpc-2) that is much lower than the canonical threshold of 0.1M⊙ yr-1 kpc-2. The wind galaxies on average have higher SFR surface densities and higher HδA values than those without strong wind signatures. The enhanced HδA indicates that bursts of star formation in the recent past are necessary for driving large-scale galactic winds. We demonstrate with Sloan Digital Sky Survey data that galaxies with high SFR surface density have experienced bursts of star formation in the recent past. Our results imply that the galactic winds revealed in our study are indeed driven by bursts of star formation, and thus probing star formation in the time domain is crucial for finding and understanding galactic winds.