Aims Quantifying β‐diversity (differences in the composition of communities) is central to many ecological studies. There are many β‐diversity metrics, falling mostly into two approaches: variance‐based (e.g., the Sørensen index), or diversity partitioning (e.g., additive β‐diversity). The former cannot be used when species–sites matrices are unavailable (which is often the case in island biogeography in particular) and only species richness data are provided. Recently, efforts have been made to partition additive β‐diversity, a metric calculated using only α‐diversity and γ‐diversity, into nestedness and turnover components (termed here “richness‐only β‐diversity partitioning”). We set out to test whether this form of β‐diversity partitioning generates interpretable results, comparable with metrics based on species incidence β‐diversity partitioning. Location: Global. Time period: Present day. Major taxa studied: Multiple taxa. Methods We first provide a brief review of β‐diversity partitioning methods, with a particular focus on the development of richness‐only β‐diversity partitioning. Second, we use 254 empirical incidence matrices (provided with the paper) sourced from the literature to measure turnover and nestedness using incidence β‐diversity partitioning, comparing the resulting values with those calculated using richness‐only β‐diversity. Results We provide an account of the emergence of β‐diversity partitioning, with particular reference to the analysis of richness‐only datasets, and to the definition and usage of the relevant metrics. Analytically, we report weak correlations between turnover and nestedness calculated using the two different approaches. We show that this is because identical values of α‐diversity and γ‐diversity can correspond to incidence matrices with a range of different structures. Main conclusions Our results demonstrate that the use of richness‐only β‐diversity partitioning to measure turnover and nestedness is problematic and can produce patterns unrelated to conventional measures of turnover and nestedness. We therefore recommend that more accurate definitions are adopted for these terms in future studies.