In this work we have analyzed the properties of a gliding dc discharge in argon at atmospheric pressure. Despite the usual designation of these discharges as 'gliding arc discharges', it was found previously that they operate in two different regimes - glow and arc. Here we analyze the differences in both regimes by means of two dimensional fluid modeling. In order to address different aspects of the discharge operation, we use two models - Cartesian and axisymmetric in a cylindrical coordinate system. The obtained results show that the two types of discharges produce a similar plasma column for a similar discharge current. However, the different mechanisms of plasma channel attachment to the cathode could produce certain differences in the plasma parameters (i.e. arc elongation), and this can affect gas treatments applications.