Gliomas, the most prevalent primary brain tumors, can be classified, depending on their characteristics, into Low-Grade Gliomas (LGG) and High-Grade Gliomas (HGG). Early detection and treatment are vital to improve the patient's prognosis, especially in HGGs, the most aggressive ones. Manually annotating MRIs to locate gliomas is a time-consuming task, leading to the development of artificial intelligence (AI) techniques that could significantly speedup and automate the process. In an effort to promote green AI, this research work proposes BTS U-Net, a novel lightweight architecture designed to streamline glioma segmentation in MRIs. We provide a comprehensive comparative analysis between BTS U-Net and four established architectures widely used in biomedical image segmentation. BTS U-Net reduces training time by 11.3% to 79.2% compared to conventional models while maintaining competitive performance, making it a more sustainable option. Additionally, it achieved comparable performance to the top-performing network among the baseline models on the BraTS 2020 dataset, with DICE scores of 0.811, 0.878, and 0.908 on the test subset and 0.790, 0.841, and 0.901 on the validation cohort for the regions enhancing tumor, tumor core, and whole tumor, respectively. Furthermore, an original analysis of the MRIs and the segmentation masks is presented, demonstrating statistical differences between HGG and LGG. Finally, we also explored the influence of the tumor type on the segmentation performance. The results suggest that a sequential two-step methodology, starting with tumor type classification followed by segmentation, could optimize performance. Therefore, the experimentation not only demonstrates the BTS U-Net's capability to balance efficiency with accuracy in glioma segmentation but also lays the groundwork for future exploration of tailored strategies based on glioma grading.