As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have recently been proposed throughout industry and academia. Yet, achieving consensus on an appropriate safety concept is still an elusive task. In this paper, we advocate for the use of Hamilton-Jacobi (HJ) reachability as a unifying mathematical framework for comparing existing safety concepts, and through elements of this framework propose ways to tailor safety concepts (and thus expand their applicability) to scenarios with implicit expectations on agent behavior in a data-driven fashion. Specifically, we show that (i) existing predominant safety concepts can be embedded in the HJ reachability framework, thereby enabling a common language for comparing and contrasting modeling assumptions, and (ii) HJ reachability can serve as an inductive bias to effectively reason, in a learning context, about two critical, yet often overlooked aspects of safety: responsibility and context-dependency.