The shapes of colloidal particles are crucial to self-assembled superstructures. Understanding the relationship between the shapes of building blocks and the resulting crystal structures is an important fundamental question. Here, we demonstrate that, by using particles whose shape interpolates between a flat disc and a sphere, not only are self-assembled superstructures but also their orientations sensitively dependent on the particle shape. By changing the shape gradually from a flat disc to a spherical shape, a crystal sequence from orientationally ordered crystals to orientationally disordered crystals with frozen and more free rotations are found. The latter two phases are identified as a glassy crystal and a plastic crystal, respectively. By combining theoretical model calculations, the formed crystal structures and the occurring transitions are found to be dictated by the interplay between particle shape and particle-particle interaction as well as particle-wall interaction. In particular, for quasi-spherical shapes, when the strong attraction dominates, a glassy crystal forms, or otherwise a plastic crystal forms. These results demonstrate that the interplay between the particle shape and the interaction can be used to tune crystallization and further fabricate colloid-based new structured and dynamic materials.