Each time a vortex enters or exits a small superconductor, a different fluxoid state develops which can be characterized by its vorticity, i.e., the number of fluxoids inside. We have studied magnetization response of such individual states and found clear signatures of first and second order transitions within the states, which reveal the existence of distinct vortex phases for a fixed number of fluxoids. We attribute the transitions to the merger of individual vortices into a single giant vortex and switching between different arrays of vortices.