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They are both ways to measure divergence in species but I'm not understanding in what exactly the differ if both use hybrid zones and gene frequencies in the study.

Clustering and Clines are two fundamentally different approaches to target the population structure problems. Because many results in classical population genetics are derived from a panmictic population, it is natural to extend them to multiple panmictic populations with some degree of gene flow in between, such as Wright's Island model and Kimura's Stepping stone model. In these discrete models, we view each subpopulation as a breeding group and hence the clustering algorithm can be used to a large number of individuals to classify them based on which subpopulation they belong to. It is 100% valid if the real population is actually discrete (such as in Galapagos), but not so if the real population is distributed continuously in space. In the latter scenario, cline may be more appropriate to describe the spatial variations of the population.

You can check Montgomery Slatkin and Nick Barton's papers on cline theory back in 1970s and 1980s to get the details, but the general property of a cline is that if divergent selection is the primary cause of the cline, then the cline steepness is proportional to the selection differences, but there is a characteristic spatial scale of variation $sigma/sqrt{s}$, below which any spatial structure will likely to be swamped by dispersal ($sigma$ is the mean dispersal distance of an individual, and $s$ is the selection intensity).So Even if the cline is a step function, which is not realistic at all, the cline will still be of finite steepness. As long as $sigma$ is not zero, you will not get a clear-cut boundary between the two sides of the population, thus invalidating the assumption of clustering algorithm. However, although clustering is not very rigorous in a continuous population, we can still use it to make qualitative explorations of our genetic data and population structure, in fact many people prefer to use that because they are conceptually clear and easy to manipulate in a computer.