In industrial IoT scenarios, attackers observe communication systems to find relations between transmitted messages and receivers, in order to conduct impersonation or man-in-the-middle attacks. Therefore, unlinkability and anonymity are desirable properties of the corresponding communications. In this paper, we connect the differential privacy (DP)-based notion, receiver-message unlinkability (RML), to the physical layer secrecy metrics for a degraded discrete memoryless broadcast channel including two receivers and an external adversary. To characterize this connection, we show that Kullback-Leibler-DP-based RML, (0,δ)-DP-based RML, strong secrecy, and distinguishing secrecy are equivalent up to a multiplicative constant. We then analyze the achievable rate region of the DP-based RML for the considered model by adapting a coding scheme which can achieve strong secrecy. A numerical comparison of the achievable rate regions of binary symmetric degraded broadcast channels under RML, strong secrecy, and a case without secrecy or privacy constraint illustrates the relationship.