Full and partial atomic electron states, atomic charges and magnetic moments in TiCo$_{2-x}$Sn ($x$ = 0, 1) are obtained using zone calculations in the FLAPW (the full-potential linearized augmented-plane-wave) model. As found, the strongly polarized 3$d$ electrons of cobalt atoms form mainly a valence band, whereas the states of the same symmetry with weak polarization of titanium electrons mainly determine the structure of the vacant state zone. As shown, the transition from alloy TiCoSn to alloy TiCo$_2$Sn is accompanied by the growth of charges and cohesive energies of atoms and increase their covalent interaction. The Heusler alloy of TiCo$_2$Sn type is a half-metal with one hundred percent polarization of Fermi electrons, while the alloy of the second type belongs to the traditional metals.