Despite recent enhancements in the deployment of differential privacy (DP), little has been done to address the human aspects of DP-enabled systems. Comprehending the complex concept of DP and the privacy protection it provides could be challenging for lay users who should make informed decisions when sharing their data. Using metaphors could be suitable to convey key protection functionalities of DP to them. Based on a three-phase framework, we extracted and generated metaphors for differentially private data analysis models (local and central). We analytically evaluated the metaphors based on experts’ feedback and then empirically evaluated them in online interviews with 30 participants. Our results showed that the metaphorical explanations can successfully convey that perturbation protects privacy and that there is a privacy-accuracy trade-off. Nonetheless, conveying information at a high level leads to incorrect expectations that negatively affect users’ understanding and limits the ability to apply the concept to different contexts. In this paper, we presented the plausible suitability of metaphors and discussed the challenges of using them to facilitate informed decisions on sharing data with DP-enabled systems.