  We investigate the properties of the double sequences of the Milky Way discs
visible in the [$\alpha$/Fe] vs [Fe/H] diagram. In the framework of Galactic
formation and evolution, we discuss the complex relationships between age,
metallicity, [$\alpha$/Fe], and the velocity components. We study stars with
measured chemical, seismic and astrometric properties from the APOGEE survey,
the Kepler and Gaia satellites, respectively. We separate the
[$\alpha$/Fe]-[Fe/H] diagram into 3 stellar populations: the thin disc, the
high-$\alpha$ metal-poor thick disc and the high-$\alpha$ metal-rich thick disc
and characterise each of these in the age-chemo-kinematics parameter space. We
compare results obtained from different APOGEE data releases and using two
recent age determinations. We use the Besan\c{c}on Galaxy model (BGM) to
highlight selection biases and mechanisms not included in the model. The thin
disc exhibits a flat age-metallicity relation while [$\alpha$/Fe] increases
with stellar age. We confirm no correlation between radial and vertical
velocities with [Fe/H], [$\alpha$/Fe] and age for each stellar population.
Considering both samples, V$_\varphi$ decreases with age for the thin disc,
while it increases with age for the h$\alpha$mp thick disc. Although the age
distribution of the h$\alpha$mr thick disc is very close to that of the
h$\alpha$mp thick disc between 7 and 14 Gyr, its kinematics seems to follow
that of the thin disc. This feature, not predicted by the hypotheses included
in the BGM, suggests a different origin and history for this population.
Finally, we show that there is a maximum dispersion of the vertical velocity,
$\sigma_Z$, with age for the h$\alpha$mp thick disc around 8 Gyr. The
comparisons with the BGM simulations suggest a more complex chemo-dynamical
scheme to explain this feature, most likely including mergers and radial
migration effects
