Atmospheric stochastic forcing associated with the North Atlantic Oscillation (NAO) and intrinsic ocean modes associated with the large-scale baroclinic instability of the North Atlantic Current (NAC) are recognized as two strong paradigms for the existence of the Atlantic Multidecadal Oscillation (AMO). The degree to which each of these factors contribute to the low-frequency variability of the North Atlantic is the central question in this paper. This issue is addressed here using an ocean general circulation model run under a wide range of background conditions extending from a super-critical regime where the oceanic variability spontaneously develops in the absence of any atmospheric noise forcing to a damped regime where the variability requires some noise to appear. The answer to the question is captured by a single dimensionless number Γ measuring the ratio between the oceanic and atmospheric contributions, as inferred from the buoyancy variance budget of the western subpolar region. Using this diagnostic, about two-third of the sea surface temperature (SST) variance in the damped regime is shown to originate from atmospheric stochastic forcing whereas heat content is dominated by internal ocean dynamics. Stochastic wind-stress forcing is shown to substantially increase the role played by damped ocean modes in the variability. The thermal structure of the variability is shown to differ fundamentally between the super-critical and damped regimes, with abrupt modifications around the transition between the two regimes. Ocean circulation changes are further shown to be unimportant for setting the pattern of SST variability in the damped regime but are fundamental for a preferred timescale to emerge.