We find, motivated by real-world applications, that the well-known request-response specification comes with multiple variations, and that these variations should be distinguished. As the first main contribution, we introduce a classification of those variations into six types, and present it as a decision tree, where a user is led to the type that is suited for their application by answering a couple of questions. Our second main contribution is the formalization of those six types in various formalisms such as grammars, temporal logics, and automata; here, two types out of the six are non-regular specifications and their formalization requires extended formalisms. We also present an overview of tools for monitoring these specifications to cater for practitioners’ needs. Through these contributions, we address an issue in formal specification that is practically important but has been scientifically somewhat overlooked.