The collisions of the isocharged sequence ions of $q=6$ (${\text{C}}^{6+}$, ${\text{N}}^{6+}$, ${\text{O}}^{6+}$, ${\text{F}}^{6+}$, ${\text{Ne}}^{6+}$, ${\text{Ar}}^{6+}$, and ${\text{Ca}}^{6+}$), $q=7$ (${\text{F}}^{7+}$, ${\text{Ne}}^{7+}$, ${\text{S}}^{7+}$, ${\text{Ar}}^{7+}$, and ${\text{Ca}}^{7+}$), $q=8$ (${\text{F}}^{8+}$, ${\text{Ne}}^{8+}$, ${\text{Ar}}^{8+}$, and ${\text{Ca}}^{8+}$), $q=9$ (${\text{F}}^{9+}$, ${\text{Ne}}^{9+}$, ${\text{Si}}^{9+}$, ${\text{S}}^{9+}$, ${\text{Ar}}^{9+}$, and ${\text{Ca}}^{9+}$) and $q=11$ (${\text{Si}}^{11+}$, ${\text{Ar}}^{11+}$, and ${\text{Ca}}^{11+}$) with helium at the same velocities were investigated. The cross-section ratios of the double-electron transfer (DET) to the single-electron capture (SEC) ${\ensuremath{\sigma}}^{\text{DET}}∕{\ensuremath{\sigma}}^{\text{SEC}}$ and the true double-electron capture (TDC) to the double-electron transfer ${\ensuremath{\sigma}}^{\text{TDC}}∕{\ensuremath{\sigma}}^{\text{DET}}$ were measured. It shows that for different ions in an isocharged sequence, the experimental cross-section ratio ${\ensuremath{\sigma}}^{\text{DET}}∕{\ensuremath{\sigma}}^{\text{SEC}}$ varies by a factor of 3. The results confirm that the projectile core is another dominant factor besides the charge state and the collision velocity in slow ($0.35\ensuremath{-}0.49{v}_{0}$; ${v}_{0}$ denotes the Bohr velocity) highly charged ions (HCIs) with helium collisions. The experimental cross-section ratio ${\ensuremath{\sigma}}^{\text{DET}}∕{\ensuremath{\sigma}}^{\text{SEC}}$ is compared with the extended classical over-barrier model (ECBM) [A. B\'ar\'any et al., Nucl. Instrum. Methods Phys. Res. B 9, 397 (1985)], the molecular Coulombic barrier model (MCBM) [A. Niehaus, J. Phys. B 19, 2925 (1986)], and the semiempirical scaling laws (SSL) [N. Selberg et al., Phys. Rev. A 54, 4127 (1996)]. It also shows that the projectile core properties affect the initial capture probabilities as well as the subsequent relaxation of the projectiles. The experimental cross-section ratio ${\ensuremath{\sigma}}^{\text{TDC}}∕{\ensuremath{\sigma}}^{\text{DET}}$ for those lower isocharged sequences is dramatically affected by the projectile core structure, while for those sufficiently highly isocharged sequences, the autoionization always dominates, hence the cross-section ratio ${\ensuremath{\sigma}}^{\text{TDC}}∕{\ensuremath{\sigma}}^{\text{DET}}$ is always small.