The Hubble parameter is a function of redshift (or time, equivalently): H(z). The Hubble constant is H_0 := H(z=0). The discrepancy is in H_0. That implies a d

The Hubble parameter is a function of redshift (or time, equivalently): H(z). The Hubble constant is H_0 := H(z=0). The discrepancy is in H_0. That implies a discrepancy at other redshifts as well, though how you connect H_0 to H(z) depends on your cosmological model. That's why the discrepancy in H_0 measurements is model-dependent. Different experiments are sensitive to the expansion rate during different epochs of cosmic history.