Observations of ionized H α gas in high-redshift disc galaxies have ubiquitously found significant line broadening, σ H α ∼ 10 -100 km s -1 . To understand whether this broadening reflects gas turbulence within the interstellar medium (ISM) of galactic discs, or arises from out-of-plane emission in mass-loaded outflows, we perform radiation hydrodynamic simulations of isolated Milky Way-mass disc galaxies in a gas-poor (low-redshift) and gas rich (high-redshift) condition and create mock H α emission line profiles. We find that the majority of the total (integrated) H α emission is confined within the ISM, with extraplanar gas contributing ∼45 per cent of the extended profile wings ( v z ≥ 200 km s -1 ) in the gas-rich galaxy. This substantiates using the H α emission line as a tracer of mid-plane disc dynamics. We investigate the relative contribution of diffuse and dense H α emitting gas, corresponding to diffuse ionized gas (DIG; ρ 0 . 1 cm -3 , T ∼ 8 000 K) and H II regions ( ρ 10 cm -3 , T ∼ 10 000 K), respectively, and find that DIG contributes f DIG 10 per cent of the total L H α . Ho we ver, the DIG can reach upwards of σ H α ∼ 60 -80 km s -1 while the H II regions are much less turbulent σ H α ∼ 10 -40 km s -1 . This implies that the σ H α observed using the full H α emission line is dependent on the relative H α contribution from DIG/H II regions and a larger f DIG would shift σ H α to higher v alues. Finally, we sho w that σ H α evolves, in both the DIG and H II regions, with the galaxy gas fraction. Our high-redshift equi v alent galaxy is roughly twice as turbulent, except for in the DIG which has a more shallow evolution.