Fragility curves are fundamental tools in seismic risk assessments, providing insights into the vulnerability of structures to earthquake-induced damages. These curves, which plot the probability of a structure reaching or exceeding various damage states against earthquake intensity, are critical for developing effective modification strategies. This review aims to present the characteristics between building- and site-specific fragility curves, which incorporate detailed local characteristics, and generic fragility curves that apply broader, more generalized parameters. We utilize the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) methodology to systematically review the literature to address key research questions about the methodological differences, applications, and implications of these curve types in assessing seismic risks. The methods involved a comprehensive search and combination of existing studies on the topic, focusing on how these curves are developed and applied in real-world scenarios. The results from this review show that building- and site-specific curves, while more precise, require extensive data and are therefore more complex and costly to develop. In contrast, generic curves, though less accurate, offer a cost-effective solution for preliminary risk assessments over large areas. The conclusions drawn from this review suggest that while each type has its merits, the choice between building- and site-specific and generic fragility curves should be guided by the specific requirements of the seismic risk assessment task, including available resources and the need for precision in the vulnerability estimations.