Understanding the surface of semiconductor nanocrystals (NCs) prepared using colloidal methods is a long-standing goal of paramount importance for all their potential optoelectronic applications, which remains unsolved largely because of the lack of site-specific physical techniques. Here, we show that multidimensional Cd-113 dynamic nuclear polarization (DNP) enhanced NMR spectroscopy allows the resolution of signals originating from different atomic and magnetic surroundings in the NC cores and at the surfaces. This enables the determination of the structural perfection, and differentiation between the surface and core atoms in all major forms of size- and shape-engineered CdSe NCs: irregularly faceted quantum dots (QDs) and atomically flat nanoplatelets, including both dominant polymorphs (zinc-blende and wurtzite) and their epitaxial nanoheterostructures (CdSe/CdS core/shell quantum dots and CdSe/CdS core/crown nanoplatelets), as well as magic-sized CdSe clusters. Assignments of the NMR signals to specific crystal facets of oleate-terminated ZB structured CdSe NCs are proposed. Significantly, we discover far greater atomistic complexity of the surface structure and the species distribution in wurtzite as compared to zinc-blende CdSe QDs, despite an apparently identical optical quality of both QD polymorphs.