Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) have emerged as a promising technology for enabling full-space signal manipulation and enhancing wireless network coverage and capacity. In this article, we present a comprehensive analytical comparison of STAR-RIS-assisted systems with single-input single-output (SISO), conventional RISs, and decode-and-forward (DF) relaying schemes, including both half-duplex (HD) and full-duplex (FD) modes. Closed-form expressions are derived for the achievable secrecy rates of STAR-RIS-aided communications under both the absence and presence of eavesdroppers. Unlike most existing works, the direct source destination link is incorporated in all considered schemes, and optimal transmit power allocation is investigated for HD and FD-DF relaying. Furthermore, we provide the conditions under which STAR-RIS outperforms HD- and FD-DF relaying and quantify the minimum number of STAR-RIS elements required to achieve superior rates. The impacts of key system parameters including transmit power, number of elements, reflection-to-transmission power ratio, element-splitting factor, and deployment positions on both achievable and secrecy performance are investigated. The results reveal that STAR-RIS systems can achieve superior rates and secrecy rates compared to all benchmark schemes.