Combining quasistatic and time-resolved transport measurements with X-ray and neutron diffraction experiments we study the non-equilibrium states that arise in pure and in Ti substituted Ca$_2$RuO$_4$ under the application of current densities. Time-resolved studies of the current-induced switching find a slow conductance relaxation that can be identified with heating and a fast one that unambiguously proves an intrinsic mechanism. The current-induced phase transition leads to complex diffraction patterns. Separated Bragg reflections that can be associated with the metallic and insulating phases by their lattice parameters, indicate a real structure with phase coexistence that strongly varies with temperature and current strength. A third contribution with a $c$ lattice constant in between those of metallic and insulating phases appears upon cooling. At low current densities, this additional phase appears below $\sim$100 K and is accompanied by a suppression of the antiferromagnetic order that otherwise can coexist with current carrying states. A possible origin of the intermediate phase is discussed.