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 Besanc{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
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