The melting-like transition in disordered sodium clusters Na-92 and Na-142 is studied by performing density functional constant-energy molecular dynamics simulations. The orbital-free version of the density functional formalism is used. In Na-142 the atoms are distributed in two distinct shells (surface and inner shells) and this cluster melts in two steps: the first one, at approximate to 130 K, is characterized by the development of a high intrashell atomic mobility, and the second, homogeneous molting at approximate to 270 K, involves diffusive motion of all the atoms across the whole cluster volume. Oil the contrary, the melting of Na-92 proceeds smoothly over a very broad temperature interval, without any abrupt change in the thermal or structural indicators. The occurrence of two steps in the melting transition is suggested to be related to the existence of a grouping of the atoms in radial shells, even if those shells present a large degree of internal disorder. It then appears that a cluster call be considered fully amorphous (totally disordered) only when there are no radial regions of low atomic density separating shells. The isomer of Na92 studied here fulfills this criterion and its thermal behavior call be considered as representative of that expected for fully amorphous clusters. Disordered Na-142, oil the other hand, that has a discernible structure of ail inner and a surface shell, should be considered as not fully disordered. The thermal behavior of these two clusters is also compared to that of icosahedral (totally ordered) sodium clusters of the same sizes.