Despite the remarkable progress in semi-supervised medical image segmentation methods based on deep learning, their application to real-life clinical scenarios still faces considerable challenges. For example, insufficient labeled data often makes it difficult for networks to capture the complexity and variability of the anatomical regions to be segmented. To address these problems, we design a new semi-supervised segmentation framework that aspires to produce anatomically plausible predictions. Our framework comprises two parallel networks: shape-agnostic and shape-aware networks. These networks learn from each other, enabling effective utilization of unlabeled data. Our shape-aware network implicitly introduces shape guidance to capture shape fine-grained information. Meanwhile, shape-agnostic networks employ uncertainty estimation to further obtain reliable pseudo-labels for the counterpart. We also employ a cross-style consistency strategy to enhance the network's utilization of unlabeled data. It enriches the dataset to prevent overfitting and further eases the coupling of the two networks that learn from each other. Our proposed architecture also incorporates a novel loss term that facilitates the learning of the local context of segmentation by the network, thereby enhancing the overall accuracy of prediction. Experiments on three different datasets of medical images show that our method outperforms many excellent semi-supervised segmentation methods and outperforms them in perceiving shape. The code can be seen at https://github.com/igip-liu/SLC-Net.