The emerging technology of fluid antenna systems (FASs) represents a promising next-generation reconfigurable antenna solution, capable of exploiting the full spatial diversity within a predefined space by finely reconfiguring the positions of radiating elements. In this paper, the performance of FAS over spatially correlated Rayleigh fading channels is investigated for two distinct scenarios: a multiple-input single-output (MISO) configuration, where a receiver with a single-antenna FAS is served by a multi-antenna transmitter (MISO-FAS), and a single-input single-output setup where single-antenna FASs are equipped at both the transmitter and receiver (Dual-FAS). Exact expressions and closed-form approximations for the outage probability (OP) of both the MISO-FAS and Dual-FAS models are derived as the core contributions of this work. To provide deeper insights into system performance, the diversity orders for each model are also derived and analyzed. Analytical results demonstrate that increasing the number of ports significantly enhances system performance. The theoretical analysis is corroborated by key findings from our simulations, demonstrating that: $i$) Both the MISO-FAS and Dual-FAS models achieve considerable performance gains as the number of ports is increased; $ii$) System performance for both configurations is inversely related to the level of port correlation; lower correlation leads to better performance; $iii$) In the high signal-to-noise ratio regime, the Dual-FAS model surpasses the performance of the MISO-FAS model.