This paper summarizes our participation in SemEval-2024 Task 8: Multigenerator, Multidomain, and Multilingual Black-Box Machine-Generated Text Detection. In this task, we aim to solve two over three Subtasks: (1) Monolingual and Multilingual Binary Human-Written vs. Machine-Generated Text Classification; and (2) Multi-Way Machine-Generated Text Classification. We conducted a comprehensive comparative study across three methodological groups: Five metric-based models (Log-Likelihood, Rank, Log-Rank, Entropy, and MFDMetric), two fine-tuned sequence-labeling language models (RoBERTA and XLM-R); and a fine-tuned large-scale language model (LS-LLaMA). Our findings suggest that our LLM outperformed both traditional sequence-labeling LM benchmarks and metric-based approaches. Furthermore, our fine-tuned classifier excelled in detecting machine-generated multilingual texts and accurately classifying machine-generated texts within a specific category, (e.g., ChatGPT, bloomz, dolly). However, they do exhibit challenges in detecting them in other categories (e.g., cohere, and davinci). This is due to potential overlap in the distribution of the metric among various LLMs. Overall, we achieved a 6th rank in both Multilingual Binary Human-Written vs. Machine-Generated Text Classification and Multi-Way Machine-Generated Text Classification on the leaderboard.