We correlate the notion of $n$-isoclinism of finite groups, introduced by J. C. Bioch in 1976, with the relative $n$-th nilpotency degree, recently studied in literature. We characterize also all the pairs which are isoclinic with $(C,D_8)$ via the relative commutativity degree $d(C,D_8)$, where $C$ is a cyclic maximal subgroup of $D_8$. A final conjecture is opened for the groups with few nontrivial values of $d(C,G)$.