In this work, new evidence and information about both the origin and evolution of filamentary structures observed in the current sheath of a small plasma focus (PF) discharge are reported. The experiments were carried out in a small generator of low energy (multipurpose generator) at the PF configuration, under different operating conditions. These include different anode and insulator geometries, without return bars and in a high-performance regime of the generator at high pressures (10 mbar). The evolution of the plasma structures is characterized by means of refractive optical techniques. The electrical behavior of the discharge, as well as its performance, are monitored with conventional electrical diagnostics and neutron and x-ray detectors, respectively. Plasma filaments of the same species are present in all tested configurations, however, in experiments with larger effective anode length (and smaller anode radii), the plasma region containing the filaments moves away from the anode surface and remains confined in a region of the plasma sheath, such as a toroidal plasma belt, without reaching the top of the anode nor participating in the radial compression phase. According to images of the plasma sheath in its early phase, the filaments originate and evolve from a precursor annular plasma formed in the lower part of the anode next to the insulator, during the process of electrical breakdown. The local character that these dense-filamentary structures acquire in the evolution of the plasma sheath would discard the current-filament hypothesis. On the other hand, experiments performed in deuterium gas with anodes of larger effective lengths and without filaments in the radial compression phase allowed the production of neutrons and x-rays at a high performance.