Here, it is shown that binary superlattices of Co/Ag nanocrystals with the same size, surface coating, differing by their type of crystallinity are governed by Co-Co magnetic interactions. By using 9 nm amorphous-phase Co nanocrystals and 4 nm polycrystalline Ag nanocrystals at 25 degrees C, triangle-shaped NaCl-type binary nanocrystal superlattices are produced driven by the entropic force, maximizing the packing density. By contrast, using ferromagnetic 9 nm single domain (hcp) Co nanocrystals instead of amorphous-phase Co, dodecagonal quasicrystalline order is obtained, together with less-packed phases such as the CoAg13 (NaZn13-type), CoAg (AuCu-type), and CoAg3 (AuCu3-type) structures. On increasing temperature to 65 degrees C, 9 nm hcp Co nanocrystals become superparamagnetic, and the system yields the CoAg3 (AuCu3-type) and CoAg2 (AlB2-type) structures, as observed with 9 nm amorphous Co nanocrystals. Furthermore, by decreasing the Co nanocrystal size from 9 to 7 nm, stable AlB2-type binary nanocrystal superlattices are produced, which remain independent of the crystallinity of Co nanocrystals with the superparamagnetic state.