Context. The transverse stratification of active galactic nuclei (AGN) jets is suggested by observations and theoretical arguments, as a consequence of intrinsic properties of the central engine (accretion disc + black hole) and external medium. On the other hand, the one-component jet approaches are heavily challenged by the various observed properties of plasmoids in radio jets (knots), often associated with internal shocks. Given that such a transverse stratification plays an important role on the jets acceleration, stability, and interaction with the external medium, it should also induce internal shocks with various strengths and configurations, able to describe the observed knots behaviours. Aims. By establishing a relation between the transverse stratification of the jets, the internal shock properties, and the multiple observed AGN jet morphologies and behaviours, our aim is to provide a consistent global scheme of the various AGN jet structures. Methods. Working on a large sample of AGN radio jets monitored in very long baseline interferometry (VLBI) by the MOJAVE collaboration, we determined the consistency of a systematic association of the multiple knots with successive re-collimation shocks. We then investigated the re-collimation shock formation and the influence of different transverse stratified structures by parametrically exploring the two relativistic outflow components with the specific relativistic hydrodynamic (SRHD) code AMRVAC. Results. We were able to link the different spectral classes of AGN with specific stratified jet characteristics, in good accordance with their VLBI radio properties and their accretion regimes. High-frequency synchrotron peaked BL Lacs, associated with advectiondominated accretion flow (ADAF) discs, are consistent with the simulations of a very weak outer jet (< 1% of the total energy) and reproduce stationary equal-distance internal shocks damped within a short distance from the central object. Flat spectrum radio quasars, associated with standard discs (optically thick, geometrically thin), have properties that are nicely reproduced by simulations of two jet components with similar energy fluxes by presenting a very strong first internal shock. Finally, low-and intermediatefrequency synchrotron peaked BL Lacs, associated with hybrid discs (ADAF in the centre and standard outer), are characterized by simulations with a relatively powerful outer jet enhancing inner stationary shocks near the core with moving shocks at large distance, accompanied by an increase in the jet aperture angle.