Yes. Nucleons and quarks represent internal degrees of freedom (DoFs) inside the nucleus resp. proton that can receive momentum-energy from a scattering electr

Yes. Nucleons and quarks represent internal degrees of freedom (DoFs) inside the nucleus resp. proton that can receive momentum-energy from a scattering electron. This is measured as a loss of the sum of the kinetic energies of the electron and its target. At low energies, the transfer to internal DoFs is negligible, so the scattering is elastic. At higher energies the transfer is relatively large, so the scattering is inelastic. At sufficiently high energy, the nucleus disintegrates into components and new particles, and in the target's centre-of-momentum frame the sum of all their kinetic energies matches the change of the electron's. But at even higher energy there is again an apparent loss of kinetic energy, so there must be further internal DoFs within the components. Those are in the proton. The higher energy scatterings are "deep". As one does deep inelastic scattering, the proton's internal DoFs absorb electron momentum-energy. At sufficiently high energy levels the proton disintegrates into many new particles. There are also differences in the scattering angle -- the amount by which the scattered electron is deflected from its beam path. Scattering angles are low in elastic scattering, and high in inelastic scattering. This gives further information about the internal DoFs. For more see Mott scattering, deep inelastic scattering, and the parton model.