Wikipedia tells us: (link)
Tau-c (also called Stuart-Kendall Tau-c) is more suitable than Tau-b for the analysis of data based on non-square (i.e. rectangular) contingency tables.
What does $\tau_c$ try to solve? More specifically, is there a problem with applying Kendall's Tau-b on non-square contingency tables? When we compute $\tau_b(x,y)$, do we implictly assume that the number of levels of $x$ is the same as the number of levels of $y$? Or is it an issue with how Tau-b omits ties?