There are many concepts and measures of beta diversity and related similarity/differentiation indices. The variance framework (derived from the total variance of a community species abundance matrix) and diversity decomposition (based on partitioning gamma diversity into alpha and beta components) are two major approaches. Chao and Chiu (2016, Methods in Ecology and Evolution, 7, 919-928) established a bridge by extending and modifying each approach so that both lead to the same classes of similarity/differentiation measures, which range in the interval [0, 1] and which can be compared across multiple sets of communities. The bridging work includes two major steps: (1) Extending the variance of community data to a class of divergence measures and use normalization to remove these measures’ constraints by alpha, gamma and total abundance. The resulting normalized divergence measures are legitimate differentiation measures. (2) Adopting a modified definition/formula of alpha diversity in the multiplicative decomposition approach based on Hill numbers; the resulting beta component can be transformed to quantify similarity/differentiation in species abundance distributions among communities. Then, the similarity/differentiation measures obtained from the extended variance framework turn out to be identical to those from the modified diversity decomposition. A real example using corals is given for illustration.