  Our paper concerns the scattering of intense laser radiation on free
electrons and it is focused on the relation between nonlinear Compton and
nonlinear Thomson scattering. The analysis is performed for a laser field
modeled by an ideal pulse with a finite duration, a fixed direction of
propagation and indefinitely extended in the plane perpendicular to it. We
derive the classical limit of the quantum spectral and angular distribution of
the emitted radiation, for an arbitrary polarization of the laser pulse. We
also rederive our result directly, in the framework of classical
electrodynamics, obtaining, at the same time, the distribution for the emitted
radiation with a well defined polarization. The results reduce to those
established by Krafft et al. [Phys. Rev. E 72, 056502 (2005)] in the particular
case of linear polarization of the pulse, orthogonal to the initial electron
momentum. Conditions in which the differences between classical and quantum
results are visible are discussed and illustrated by graphs.
