In a diamond, the carbon atoms are arranged tetrahedrally. Each carbon atom is attached to four other carbon atoms 1.544 x 10-10 meter away with a C-C-C bond angle of 109.5 degrees. It is a strong, rigid three-dimensional structure that results in an infinite network of atoms.
It is not exactly a FCC structure.
ZnS occurs in two common polytypes, zincblende (also called sphalerite) and wurtzite.
Zincblende/sphalerite is based on a fcc lattice of anions whereas wurtzite is derived from an hcp array of anions. In both structures, the cations occupy one of the two types of tetrahedral holes present.
Structure of ZnS and diamond is kind of similar.