Both limited annotation and domain shift are significant challenges frequently encountered in medical image segmentation, leading to derivative scenarios like semi-supervised medical (SSMIS), semi-supervised medical domain generalization (Semi-MDG) and unsupervised medical domain adaptation (UMDA). Conventional methods are generally tailored to specific tasks in isolation, the error accumulation hinders the effective utilization of unlabeled data and limits further improvements, resulting in suboptimal performance when these issues occur. In this paper, we aim to develop a generic framework that masters all three tasks. We found that the key to solving the problem lies in how to generate reliable pseudo labels for the unlabeled data in the presence of domain shift with labeled data and increasing the diversity of the model. To tackle this issue, we employ a Diverse Teaching and Label Propagation Network (DTLP-Net) to boosting the Generic Semi-Supervised Medical Image Segmentation. Our DTLP-Net involves a single student model and two diverse teacher models, which can generate reliable pseudo-labels for the student model. The first teacher model decouple the training process with labeled and unlabeled data, The second teacher is momentum-updated periodically, thus generating reliable yet divers pseudo-labels. To fully utilize the information within the data, we adopt inter-sample and intra-sample data augmentation to learn the global and local knowledge. In addition, to further capture the voxel-level correlations, we propose label propagation to enhance the model robust. We evaluate our proposed framework on five benchmark datasets for SSMIS, UMDA, and Semi-MDG tasks. The results showcase notable improvements compared to state-of-the-art methods across all five settings, indicating the potential of our framework to tackle more challenging SSL scenarios.