Fluid antenna systems (FAS) offer a promising paradigm for enhancing wireless communication by exploiting spatial diversity, yet a rigorous analytical framework for their error probability has been notably absent. To this end, this paper addresses this critical gap by unveiling the \textbf{fundamental scaling laws} that govern the symbol error rate (SER) of FAS in realistic, spatially correlated channels. To establish these laws, we derive a tight, closed-form asymptotic expression for the SER applicable to a general class of modulation schemes. This result is pivotal as it establishes the fundamental scaling law governing the relationship between SER and the channel's spatial correlation structure. Based on this framework, we provide a complete characterization of the diversity and coding gains. The analysis culminates in a definitive design directive: SER can be fundamentally improved by expanding the antenna's movement space to increase diversity, while merely increasing port density within a constrained space yields diminishing returns.