It is well-known that long-range order cannot occur in 1d magnetic systems with short-range interactions. A remanent magnetization may, however, be observed in some anisotropic spin chains due to slow dynamics. The physics of such systems -- named Single-Chain Magnets -- is mainly dictated by the temperature dependence of the relaxation time (tau) and the correlation length (xi). A simple random-walk argument relates these two quantities with each other: within a time tau a domain wall performs a random walk over a distance xi. Depending on the relative strength of the exchange interaction and the single-ion anisotropy, the relevant excitations consist either of (extending over just one lattice spacing) or (extending over several lattice constants) domain walls. By combining time-quantified Monte-Carlo simulations with the transfer-matrix technique, we highlighted that the broad- and sharp-wall regimes are associated with different temperature dependences i) of the correlation length and ii) of the diffusion coefficient of domain-wall motion. These findings allows us to explain the different relationship between tau and xi reported for broad- and sharp-wall Single-Chain Magnets.