  Observations of ionised H$\alpha$ gas in disc galaxies with high star
formation rates have ubiquitous and significant line broadening with widths
$\sigma_{\rm H\alpha}\gtrsim 50-100\ {\rm km\ s^{-1}}$. To understand whether
this broadening reflects gas turbulence within the interstellar medium (ISM) of
galactic discs, or arises from off-the-plane emission in mass-loaded galactic
winds, 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 H$\alpha$ emission line profiles. We
find that the vast majority of the ${\rm H\alpha}$ emission is confined within
the ISM, with extraplanar gas contributing mainly to the extended profile
wings. This substantiates the \Halpha emission line as a tracer of mid-plane
disc dynamics. We investigate the relative contribution of diffuse and dense
${\rm H\alpha}$ emitting gas, corresponding to DIG ($\rho \lesssim 0.1\ {\rm
cm^{-3}}$, $T\sim 8\ 000\ {\rm K}$) and HII regions ($\rho \gtrsim 10\ {\rm
cm^{-3}}$, $T\sim 10\ 000\ {\rm K}$), respectively, and find that DIG
contributes $\lesssim 10 \%$ of the total ${\rm L}_{\rm H\alpha}$. However, the
DIG can reach upwards of $\sigma_{\rm H\alpha} \sim 60-80\ {\rm km\ s^{-1}}$
while the HII regions are much less turbulent $\sigma_{\rm H\alpha}\sim10-40\
{\rm km\ s^{-1}}$. This implies that the $\sigma_{\rm H\alpha}$ observed using
the full ${\rm H\alpha}$ emission line is dependent on the relative ${\rm
H\alpha}$ contribution from DIG/HII regions and a larger $f_{\rm DIG}$ would
shift $\sigma_{\rm H\alpha}$ to higher values. Finally, we show that
$\sigma_{\rm H\alpha}$ 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.
