[en] The spinning electron model by Barut and Zanghi, which has been recently translated into the Clifford algebra language is used as a starting point to this work. Such a translation is 'completed', first of all, by expressing in the Clifford formalism the original Barut-Zanghi (BZ) solution, which referred (at the classical limit) to an internal helical motion with a time-like speed, and is here shown to originate from the superposition of positive and negative energy solutions of the Dirac equation (when restricted to the helical path). Moreover, in this paper a general method for constructing solutions of the Dirac equation is yielded which represent at the classical limit time-like motions along a cylindrical helix. Then, it is shown how to construct solutions of the Dirac equation describing helical motions with light-like speed, which meet very well the standard interpretation of the velocity operator in the Dirac equation theory (and agree with Hestenes' solution, even if that author reached it via ad-hoc assumptions that are unnecessary in the present approach). All solutions are analysed also in their quantum version. The above results appear to support the conjecture that the Zitterbewegung motion (a helical motion, at the classical limit) is really responsible for the electron spin. (author)