The Atlantic Meridional Overturning Circulation (AMOC) is one of the most essential mechanisms influencing our climate system. By comparing constant depth (z-AMOC) and density (ρ-AMOC) frameworks under pre-industrial, historical and abrupt 4xCO₂ scenarios we analyze how the circulation mean state and variability differ amongst them. Water mass transformations are also assessed as a matter of analyzing surface-induced and interior-mixing-induced transformations. As expected, both location and strength of AMOC maxima are deeply affected by the framework choice, with the AMOC reaching a maximum transport of 21 Sv at around 35°N under constant depth coordinates, as opposed to ∼25 Sv at 55°N when diagnosed from density surfaces for both pre-industrial and historical climate. When quadrupling the CO₂, both frameworks exhibit an abrupt AMOC weakening followed by a steady recovery to maximum values of 10-15 Sv. The z-AMOC maxima timeseries correlates more with those at 26°N (r ∼0.7) than with the ρ-AMOC maxima (r ∼-0.3), due to the flatter isopycnals in the z framework even in the subpolar North Atlantic, where isopycnals are, in fact, steeper. Based on this discrepancy, we argue that the density framework is more coherent to the physics of this circulation by directly incorporating water mass transformations and their density structure. We suggest that more analysis across timescales and under different conditions must be performed with density surface outputs being provided by as many models as possible, to enable a more comprehensive analysis of these two frameworks and their applications.