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 of the random phase-shift configuration and the independent phase-shift model, which constitute performance lower and upper bounds, respectively. Then, the diversity order of each strategy is investigated based on the obtained analytical results. It is shown that the proposed DP-PSC strategy achieves full diversity order simultaneously for users located on both sides of the STAR-RIS. Moreover, power scaling laws are derived for the three proposed strategies and for the random phase-shift configuration. Numerical simulations reveal a performance gain if the users on both sides of the STAR-RIS are served by NOMA instead of OMA. Moreover, it is shown that the proposed DP-PSC strategy yields the same diversity order as achieved by STAR-RISs under the independent phase-shift model and a comparable power scaling law with only 4 dB reduction in received power.