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A correlated transmission and reflection (T&R) phase-shift model is proposed for passive lossless simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs). A STAR-RIS-aided two-user downlink communication system is investigated for both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA). To evaluate the impact of the correlated T&R phase-shift model on the communication performance, three phase-shift configuration strategies are developed, namely the primary-secondary phase-shift configuration (PS-PSC), the diversity preserving phase-shift configuration (DP-PSC), and the T/R-group phase-shift configuration (TR-PSC) strategies. Furthermore, we derive the outage probabilities for the three proposed phase-shift configuration strategies as well as for those for the random phase-shift configuration and the independent phase-shift model, which …