Tuberculosis encompasses a spectrum of characteristics—including bacillary burden, clinical severity, and access to care—that are relevant to clinical and epidemiological outcomes and the performance of diagnostic assays. The value of diagnostic assays depends not only on their numerical accuracy, which can vary substantially between populations, but also on which individuals with and without tuberculosis the assays identify. Moreover, detectable features of tuberculosis, such as pathogen burden or host responses, are often correlated, making it difficult to predict the accuracy and impact of diagnostic algorithms from the accuracies of individual component tests. Therefore, when evaluating novel tuberculosis diagnostics, greater consideration should be given to characterising which segments of the disease spectrum are detected, how these segments overlap across tests, and how they are prioritised for detection. Understanding these relationships is particularly crucial for screening, given that screening seeks to detect a broad spectrum of disease and often uses multistep algorithms. We present a framework for understanding the sensitivity and specificity of assays and algorithms as the degree of alignment between different subsets of the disease spectrum. Based on this framework, we make recommendations for the measurement, reporting, target setting, and interpretation of diagnostic accuracy to guide both novel test development and the optimal use of existing diagnostics.