Over the past decades, the neuropsychological science community has endeavored to determine the number and nature of distinguishable human cognitive abilities. Based on covariance structure analyses of inter-individual performance differences in multiple cognitive tasks, the ability structure has been substantiated with sufficient consensus. However, there remains a crucial open question that must be answered to develop unified theoretical views and translations toward neuropsychological applications: Is the cognitive ability structure ascertained at the behavioral level similarly reflected in the anatomical and functional properties of the brain? In the current study, we explored the cognitive ability structure derived from positive and negative networks reflected by the brains anatomical properties (thickness, myelination, curvature, and sulcus depth) that were found to be associated with performance in 15 cognitive tasks. The derived neurometric ontological structure was contrasted with the entities of psychometric ontology. Overall, we observed that the brain-derived ontological structures are partly consistent with each other, but also show interesting differences that complement the psychometric ontology. Moreover, we discovered that brain areas associated with the inferred abilities are segregated, with little or no overlap between abilities. Nevertheless, they are also integrated as they are densely connected by white matter projections with an average connection density higher than the brain connectome. The consistency and differences between psychometric and neurometric ontologies are crucial for theory building, diagnostics, and neuropsychological therapy, which highlights the need for the simultaneous and complementary consideration.