In this work, within the framework of a unified model for the discharge gap and electrodes, a comparative numerical analysis was carried out on the effect of evaporation of graphite anode material on the characteristics of the arc discharge in helium and argon. The effect of changing the plasma-forming ion, in which the ion of evaporated atomic carbon becomes the dominant ion, is demonstrated. For an arc discharge in helium, this effect is accompanied by a jump-like change in the dependence of the current density on voltage (CVC), and smoothly for a discharge in argon. With regard to the dynamics of the ignition of an arc discharge, it is shown that during the transition from glow discharge to arc in helium, the discharge parameters are also accompanied by an abrupt change, while in argon, this transition is smooth. This is due to the fact that the ionization potentials, as well as the ionization cross sections, differ significantly for helium and carbon, and are close in value for helium and argon. For various points on the CVC, the density distributions of the charged and neutral particles of an inert gas and evaporated gases are presented.