Restricted normal cones are of interest, for instance, in the theory of local error bounds, where they have recently been used to characterize the existence of a constrained Lipschitzian error bound. In this paper, we establish relations between two concepts for restricted normals. The first of these concepts was introduced in the late 1990s by Studniarski, the second more than ten years later by Bauschke et al. Under assumptions, suitable for the use in the theory of error bounds, we explain that the two concepts are the same. Furthermore, we develop several formulas that simplify the computation of restricted normals.