Physics of the near-cathode plasma layer in high-pressure discharge lamps is considered. Hierarchy of macroscopic length scales and various mean free paths has been analyzed. It has been shown that current transfer to cathodes of high-pressure discharge lamps may occur in two physically different regimes, one of them being a regime of a weakly ionized plasma with the electron temperature close to the heavy-particle temperature, and another being a regime of moderately to strongly ionized plasma with the electron temperature much higher than the heavy-particle temperature. For the first regime, the ion current coming from the quasineutral plasma to the space-charge sheath edge has been calculated. It has been found that this current is by several orders of magnitude lower than the experimentally measured values of the current density to the cathode. Calculations for the second regime have been made on the basis of the preceding model of Benilov and Marotta. It has been shown that regimes of a diffuse current transfer to cathodes of arc lamps may be explained by means of this model as regimes with moderately ionized plasmas, while the hot-spot regimes may be explained as regimes with fully ionized plasmas.