The results of the calculation of the electronic and magnetic properties of the perovskite ${\text{CaCrO}}_{3}$ in the local spin-density approximation (LSDA) and local spin-density with the account of on-site Coulomb correlations $(\text{LSDA}+U)$ approximations are presented. Both approaches provide correct magnetic ground state [$C$-type antiferromagnet ($\text{AFM-}C$)], but electronic structure is rather different: metallic in LSDA and insulating in $\text{LSDA}+U$. The character of magnetic interactions and the mechanism of stabilization of the AFM-$C$ structure are also qualitatively different: if in LSDA it is a Stoner-like band magnetism with a rather strong next-nearest-neighbor (``diagonal'') exchange, in $\text{LSDA}+U$ it is due to a superexchange interaction of localized electrons with an orbital ordering thereof. As one can conclude from both theoretical and experimental results, apparently ${\text{CaCrO}}_{3}$ is in a crossover regime between localized and itinerant electrons.