The detection of texts generated by LLMs has quickly become an important research problem. Many supervised and zero-shot detectors have already been proposed, yet their effectiveness and precision remain disputed. Current research therefore focuses on making detectors robust against domain shifts and on building corresponding benchmarks. In this paper, we show that the actual limitations hindering progress in LLM detection lie elsewhere: LLM detection is often implicitly modeled as an authorship attribution task, while its true nature is that of authorship verification. We systematically analyze the current research with respect to this misunderstanding, conduct an in-depth comparative analysis of the benchmarks, and validate our claim using state-of-the-art LLM detectors. Our contributions open the realm of authorship analysis technology for understanding and tackling the problem of LLM detection.