Terrestrial free-space optical (FSO) communication systems, while designed to operate on large unlicensed optical bandwidths, are fundamentally power-constrained due to stringent eye-safety regulations. Moreover, channel fluctuations inherent to terrestrial FSO links further reduce the received optical power. Consequently, the achievable signal-to-noise ratio (SNR) per hertz could become limited, especially for future terrestrial FSO systems based on coherent communications. This necessitates the development of efficient and adaptive communication strategies at both the optical transmitter and receiver. However, a comprehensive assessment of adaptive coherent terrestrial FSO systems remains largely unexplored in the existing literature. This paper investigates terrestrial FSO communication links employing adaptive coherent transmission and synchronous heterodyne detection-based reception operating in the shot-noise-limited regime. Specifically, we propose a novel exact closed-form expression for the average spectral efficiency limit of coherent FSO communication systems with optimal adaptive signaling over gamma-gamma turbulence channels with pointing errors. More importantly, we provide a detailed assessment of the impact of turbulence and pointing error impairments on the coherent FSO system performance, revealing several novel and counterintuitive insights. Extensive numerical results help elucidate the intricacies of analyzing these terrestrial FSO systems and clarify a few misconceptions alluded to in recent related literature.