The isotopic-yield distributions and kinematic properties of fragments produced in transfer-induced fission of 240Pu and fusion-induced fission of 250Cf, with 9 MeV and 45 MeV of excitation energy respectively, were measured in inverse kinematics with the spectrometer VAMOS. The kinematic properties of identified fission fragments allow to derive properties of the scission configuration such as the distance between fragments, the total kinetic energy, the neutron multiplicity, the total excitation energy, and, for the first time, the proton- and neutron-number sharing during the emergence of the fragments. These properties of the scission point are studied as functions of the fragment atomic number. The correlation between these observables, gathered in one single experiment and for two different fissioning systems at different excitation energies, give valuable information for the understanding and modeling of the fission process.