Submicron step-edge Josephson junctions in YBa2Cu3O7−δ (YBCO) thin films were fabricated and studied. All measured junctions fall into three categories: low critical current resistively shunted Josephson junctions, intrinsic Josephson junctions, and quasiparticle tunnel junctions. The transport in the junctions is correlated with the microstructure of YBCO films grown on the step edge. We argue that the properties of conventional step-edge junctions can be understood as a superposition of those types.