In this paper, the correlation coefficient between the ion fluxes in the solar wind and the magnetosheath is analyzed with the use of data of two satellites of the THEMIS mission and the THEMIS/Spektr-R satellites obtained in 2008 and 2011−2014, respectively. We have distinguished the conditions in which a high level of correlation between the measurements in the solar wind and the magnetosheath is observed, i.e., the correlation coefficient exceeds 0.7. As key factors, we consider both direct parameters of the solar wind, such as the density, the magnetic field magnitude, the magnetosonic Mach number, and the ratio β of the thermal pressure to the magnetic, and a more general factor—the type of large-scale structure of the solar wind. In addition, the effect of the satellite location in the magnetosheath relative to its boundaries—the bow shock and the magnetopause—on the correlation level is considered. It has been shown that, in roughly one third of cases, the plasma structures of the solar wind undergo a strong modification at the bow shock and in the magnetosheath, which results in a low correlation level corresponding to a correlation coefficient of less than 0.5; a high correlation level is observed in half of cases, i.e., the plasma structures are weakly disturbed. It has been determined that (1) the low correlation level in the magnetosheath behind quasi-perpendicular bow shock is more often observed near the magnetopause than in region just behind the bow shock, (2) the probability of observations of a high correlation level is independent of the profile shape of the quasi-perpendicular bow shock, and (3) the high correlation is more probable for the events corresponding to the solar wind of the Corotating Interaction Region (CIR) type than for those with the other solar wind types observed in the considered period.