Seismic risk assessment in school buildings is critical for ensuring the safety and resilience of educational institutions against seismic events. This paper presents a new seismic risk methodology named MM Risk and comparative study with Adriseismic methodology used for seismic risk assessment. The study aims to provide insights into the effectiveness and reliability of these methods in evaluating the seismic vulnerability of school buildings. Through a comprehensive review of the existing literature and application on a dataset of 213 schools (367 buildings), this paper evaluates the strengths and limitations of each method in terms of accuracy, complexity, and practical applicability. The results show that by integrating the approach of Adriseismic methodology and incorporating extensions related to irregularities, the social risk component (number of users), and the ability to assess different types of structures, a comprehensive and tailored methodology for assessing seismic risk can be developed. This is important since these factors are strongly influencing the seismic risk of schools as connected systems. Furthermore, this paper explores the implications of these findings for improving seismic risk mitigation strategies in school buildings. MM Risk methodology places over 70% of school buildings in the medium seismic risk category and 27% in the high seismic risk category. On the other hand, the Adriseismic methodology is more stringent, classifying 60% of school buildings into high and very-high risk categories. This disparity undoubtedly influences the prioritization list for seismic risk mitigation measures. However, definitely the comparative analysis presented in this paper offers valuable guidance for engineers, policymakers, and stakeholders involved in the seismic retrofitting and design of school buildings, ultimately contributing to the enhancement of seismic resilience in educational infrastructure.