Graph data is increasingly prevalent across domains, offering analytical value but raising significant privacy concerns. Edges may encode sensitive relationships, while node attributes may contain sensitive entity or personal data. Differential Privacy (DP) has gained traction for its strong guarantees, yet applying DP to graphs is challenging because of their complex relational structure, leading to trade-offs between privacy and utility. Existing methods vary in privacy definitions, utility goals, and contextual settings, complicating comparison. For practitioners, this is compounded by DP's interpretability issues, contributing to misleading protection claims. To address this, we propose a novel systemisation of existing methods tailored to practical considerations and adaptable to varying practitioner objectives. Our contributions include: (i) a comprehensive survey of differentially private graph release methods; (ii) identification of key vulnerabilities; and (iii) a practitioner-oriented, objective-based framework to guide the selection, interpretation, and sound evaluation of existing methods. We demonstrate the use of our systemisation through two exemplary scenarios in which we assume the role of a social network analyst, apply it, and conduct evaluations in accordance with our framework. Together, these two illustrative instantiations ultimately provide a unified benchmark for state-of-the-art methods in the social networks domain.