The original version of this manuscript included some portions of text from the first submitted version. Such text had been modified in response to the referee’s comments, and appeared erroneously in the final version. Therefore, the original manuscript has been replaced with an updated version for final publication. The presentation and interpretation of the results has been reordered and modified in order to provide a more logical description of the main points and to clarify the overall conclusions. All of the above modifications had been presented in the authors’ response to the referee’s comments. A list of the most relevant changes is given below. (i) In the abstract, the concluding sentence has been modified to explicitly account for the observed difference between the early stage of turbulence in the magnetospheric boundary layer and the more developed one in the magnetosheath. (ii) In section 3, the text was considerably reordered for a clearer reading.Abetter descriptionwas given for the low-frequency spectra, indicating shallow power with bumps related to the Kelvin-Helmoltz instability (KH), and a dominance of the velocity spectrum in the magnetosheath. In the description of the inertial range of frequencies, we added a comment on the possible role of the KH in generating the boundary layer turbulence, and added some references corroborating our observation. Finally, a concluding overall remark was added pointing out the weak observed level of turbulence in both regions. (iii) In section 4, we have reordered and condensed the text for a smoother reading. In the description of the results, we have now explicitly mentioned that the main observation is that overall intermittency is low in both intervals, although the scaling properties of the kurtosis suggests that nonlinear interactions are rapidly building small-scale intermittency. We have removed the direct comparison of the intermittency in the two intervals. (iv) In section 5, we have added a paragraph reinterpreting the observed difference between the two regions in terms of third-order moment scaling, and in particular concluding that the boundary layer interval shows a strong active nonlinear interaction that are quickly generating a turbulent cascade, as evidenced by the large values of the energy transfer rate for this region. (v) In section 6, we have extended the above comment on the global energy transfer to the distribution of the local proxy. (vi) Finally, in the Conclusions we have removed the comparison of the intermittency of the different fields components in the two regions, according to the changes in section 4, and have replaced the text with a more general description of the low intermittency level in both samples, indicating the ongoing process of generation of the turbulent cascade. We have also expanded the interpretation of the Politano-Pouquet law results, adding a new interpretation in terms of evolving turbulence and of a more effective nonlinear cascade being active in the boundary layer. This paper has been typeset from a Microsoft Word file prepared by the author.