The non-linear turbulent regimes in the tokamak scrape-off layer (SOL) are identified according to the linear instability responsible for the perpendicular transport. Four regions of the SOL operational parameters are determined where turbulence is driven by the inertial or resistive branches of the ballooning mode or of drift waves. The analysis, based on the linear electrostatic drift-reduced Braginskii equations, evaluates the pressure scale length self-consistently from the balance between plasma losses at the vessel and perpendicular turbulent transport. The latter is estimated by assuming that turbulence saturation occurs due to a local flattening of the plasma gradients and associated removal of the linear instability drive; it is also shown that transport is led by the mode that maximizes the ratio of the linear growth to the poloidal wavenumber. The methodology used to identify the turbulent regimes is confirmed by the results of non-linear simulations of SOL turbulence. The identification of the turbulent regimes, the predicted pressure scale length, and the poloidal wavenumber of the leading mode are in reasonable agreement with non-linear simulation results.