Spatiotemporal oscillations confined to quasi-2D surface layers or 3D volumes play an important role for wave-based information relay and global oscillations in living systems. Here, we describe experiments with the Belousov-Zhabotinsky reaction confined to microbeads, in which the catalyst is selectively loaded either onto the surface or into the body of the spherical beads. We find that the dynamics of global oscillations, traveling reaction fronts, and rotating spiral waves under surface confinement are strikingly different from those in the bead volume. Our results establish a useful model system for the study of geometrical effects on nonlinear chemical processes and provide diagnostic features that allow the distinction of membrane-mediated 2D and cytosolic 3D processes in biological cells.