We contribute to recent discussions about the role of invariance testing in cultural, multi-group and longitudinal research by highlighting that these debates obscure two different questions. Most researchers are interested in the quality of a first mapping process of concepts onto numerals, that is the quality of measurement. Due to a lack of independent data, researchers typically resort to a second mapping, focusing on the differential item functioning of items relative to each other. This second mapping links items to proposed constructs and the question is about symmetry of observational patterns across measurement occasions. Importantly, additional theoretical assumptions are invoked during this process, which can be queried through invariance testing. Using multiple items to index a shared construct is quite a different question compared to what researchers typically want to know, namely, whether the measurement process itself is free of bias. We argue that invariance testing is a theory-testing process rather than a pure methodological tool. We use three examples to highlight that a) the two mapping processes are distinct and b) that paying attention to invariance as the second mapping process is of theoretical (and not just methodological) interest for researchers interested in culture, over and above a concern with the first mapping. We also briefly discuss a third mapping process, which has been suggested as an alternative to invariance testing. We highlight shortcomings of these recent recommendations. Our plea is that researchers pay more attention to invariance testing as a theory-guided process.