Hard carbon is the leading candidate anode for commercialization of Na-ion batteries. Hard carbon has a unique local atomic structure, which is composed of nanodomains of layered rumpled sheets that have short-range local order resembling graphene within each layer but complete disorder along the caxis between layers. A primary challenge holding back the development of Na-ion batteries is that a complete understanding of the structure-capacity correlations of Na-ion storage in hard carbon has remained elusive. This article presents two key discoveries: first that characteristics of hard carbon's structure can be modified systematically by heteroatom doping, and second, that these structural changes greatly affect Na-ion storage properties, which reveals the mechanisms for Na storage in hard carbon. Specifically, via P or S doping, the interlayer spacing is dilated, which extends the low-voltage plateau capacity, while increasing the defect concentrations with P or B doping leads to higher sloping sodiation capacity. Our combined experimental studies and first principles calculations reveal that it is the Na-ion-defect binding that corresponds to the sloping capacity, while the Na intercalation between graphenic layers causes the low-potential plateau capacity. The new understanding provides a new set of guiding principles to optimize hard carbon for Na-ion battery applications.