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We present magnetization and (1)H nuclear magnetic resonance (NMR) measurements performed in both closed Cr8 and open Cr8Zn antiferromagnetic molecular rings in the temperature range 1.65  <  T  <  300 K at different external magnetic fields. The magnetization measurements on Cr8Zn are consistent with a small decrease of the exchange constant J(Cr-Cr) and a much smaller gap between the singlet ground state and the first magnetic excited state when compared with the same properties of the closed ring Cr8, in agreement with previous inelastic neutron scattering results. The temperature dependence of the (1)H NMR nuclear spin lattice relaxation rate (NSLR), 1/T1(T), was found to be similar in both open and closed rings with a magnetic field dependent peak centered at a temperature of the order of the corresponding exchange constant J(Cr-Cr). Such main peak in the NSLR could be fitted with a single correlation frequency ω(c1) as in most molecular magnets. At low temperature T  <  4 K, a new feature not observed in previous NMR measurements on antiferromagnetic rings and consisting in a smaller peak of 1/T1(T) which is well resolved only in Cr8Zn, was singled out. This low-T peak indicates the presence of a second correlation frequency ω(c2) of the magnetization, found to be quite different between the two rings and thus possibly reflecting the different low temperature level structure associated with the different spin topology. The presence of ω(c2) is confirmed by the NMR spin-spin relaxation rate enhancement, which generates a two-steps wipe-out effect of the NMR signal intensity.