Test-negative studies recruit cases who attend a healthcare facility and test positive for a particular disease; controls are patients undergoing the same tests for the same reasons at the same healthcare facility and who test negative. The design is often used for vaccine efficacy studies, but not exclusively, and has been posited as a separate type of study design, different from case-control studies because the controls are not sampled from a wider source population. However, the design is a special case of a broader class of case-control designs that identify cases and sample "other patient" controls from the same healthcare facilities. Therefore, we consider that new insights into the test-negative design can be obtained by viewing them as case-control studies with "other patient" controls; in this context, we explore differences and commonalities, to better define the advantages and disadvantages of the test-negative design in various circumstances. The design has the advantage of similar participation rates, information quality and completeness, referral/catchment areas, initial presentation, diagnostic suspicion tendencies, and preferences by doctors. Under certain assumptions, valid population odds ratios can be estimated with the test-negative design, just as with case-control studies with "other patient" controls. Interestingly, directed acyclic graphs (DAGs) are not completely helpful in explaining why the design works. The use of test-negative designs may not completely resolve all potential biases, but they are a valid study design option, and will in some circumstances lead to less bias, as well as often the most practical one.