Abstract Observations of ionised Hα gas in high-redshift disc galaxies have ubiquitously found significant line broadening, σHα ∼ 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 (RHD) simulations of isolated Milky Way-mass disc galaxies in a gas-poor (low-redshift) and gas rich (high-redshift) condition and create mock Hα emission line profiles. We find that the majority of the total (integrated) Hα emission is confined within the ISM, with extraplanar gas contributing $\sim 45~{{\%}}$ of the extended profile wings (vz ≥ 200${\, \rm {km\, s^{-1}} }$) in the gas-rich galaxy. This substantiates using the Hα emission line as a tracer of mid-plane disc dynamics. We investigate the relative contribution of diffuse and dense Hα emitting gas, corresponding to diffuse ionised gas (DIG; ρ ≲ 0.1 cm−3, T ∼ 8 000 K) and HII regions (ρ ≳ 10 cm−3, T ∼ 10 000 K), respectively, and find that DIG contributes $f_{\rm DIG}\lesssim 10~{{\%}}$ of the total LHα. However, the DIG can reach upwards of σHα ∼ 60 − 80 km s−1 while the HII regions are much less turbulent σHα ∼ 10 − 40 km s−1. This implies that the σHα observed using the full Hα emission line is dependent on the relative Hα contribution from DIG/HII regions and a larger fDIG would shift σHα to higher values. Finally, we show that σHα evolves, in both the DIG and HII regions, with the galaxy gas fraction. Our high-redshift equivalent galaxy is roughly twice as turbulent, except for in the DIG which has a more shallow evolution.