The capture-fission cross-sections in an energy range of 206-242 MeV of 48Ca-projectiles and mass-energy distributions (MEDs) of reaction products in an energy range of 211-242 MeV have been measured in the 48Ca+208Pb reaction using the double-arm time-of-flight spectrometer CORSET. The MEDs of fragments for heated fission were shown to consist of two components. One component, which is due to classical fusion-fission, is associated with the symmetric fission of the 256No compound nucleus. The other component, which appears as shoulders, is associated with the quasi-fission process and can be named quasi-fission shoulders. Those quasi-fission shoulders enclose light fragments whose masses are 60-90 a.m.u. The total kinetic energy (TKE) of the fragments that belong to the shoulders is higher than the value expected for a classical fusion-fission process. We have come to the conclusion that in quasi-fission, spherical shells with Z=28 and N=50 play a great role. It has also been demonstrated that the properties of the MEDs of fragments formally agree with a well-known hypothesis of two independent fission modes; in this case the modes are normal fusion-fission and quasi-fission processes. A high-energetic Super-Short mode of classical fission has been found at low excitation energies in the mass range of heavy fragments M = 130-135 and TKE = 233 MeV; however the yield associated with this mode is small.