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We investigate the properties of the double sequences of the Milky Way discsvisible in the [$\alpha$/Fe] vs [Fe/H] diagram. In the framework of Galacticformation and evolution, we discuss the complex relationships between age,metallicity, [$\alpha$/Fe], and the velocity components. We study stars withmeasured 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, thehigh-$\alpha$ metal-poor thick disc and the high-$\alpha$ metal-rich thick discand characterise each of these in the age-chemo-kinematics parameter space. Wecompare results obtained from different APOGEE data releases and using tworecent age determinations. We use the Besan\c{c}on Galaxy model (BGM) tohighlight selection biases and mechanisms not included in the model. The thindisc exhibits a flat age-metallicity relation while [$\alpha$/Fe] increaseswith stellar age. We confirm no correlation between radial and verticalvelocities 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 agedistribution of the h$\alpha$mr thick disc is very close to that of theh$\alpha$mp thick disc between 7 and 14 Gyr, its kinematics seems to followthat of the thin disc. This feature, not predicted by the hypotheses includedin 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. Thecomparisons with the BGM simulations suggest a more complex chemo-dynamicalscheme to explain this feature, most likely including mergers and radialmigration effects

Deciphering the evolution of the Milky Way discs: Gaia APOGEE Kepler giant stars and the Besan\c{c}on Galaxy Model