The correlation energies of the helium isoelectronic sequence (IS) and of Hooke's IS are very similar and are both weakly increasing upon increasing the nuclear charge/force constant, respectively. However, their separation into radial and angular correlations shows interesting differences. First, for intermediate (and high) values of the force constant radial correlation in Hooke's IS is surprisingly low. Second, both systems exhibit a decrease in the relative contribution of radial versus angular correlation upon strengthening the one-body attractive potential; however, unlike the helium IS, in Hooke's IS the radial correlation energy increases in absolute value upon strengthening the attractive one-body potential. The contribution of radial correlation to the Coulomb hole is examined and the asymptotic behavior at both strong and weak attractive potentials is considered. Radial correlation in Hooke's IS is found to constitute about 9.3% of the total correlation energy when the spring constant approaches the limit k-->infinity, but 100% of the total correlation energy for k-->0. Our results highlight both the similarities and the differences between the helium and Hooke's ISs.