Semi-supervised learning (SSL) is increasingly employed in medical image segmentation, primarily due to the scarcity of well-labeled data, which necessitates precise and technical annotations at the pixel level. This study aims to elucidate task-invariant and task-specific dependencies among common representation tasks. Initially, strong and weak correlation tasks from various levels are categorized with respect to the pixel-level segmentation. Subsequently, we introduce the Task-Aware Smoothness (TAS) Assumption, which capitalizes on task-aware perturbations within a single model while promoting task-aware consistency across correlated tasks. Building upon this assumption, we propose a novel Unified Task-aware Consistency (UniTask) framework to simultaneously unify and reinforce both strong and weak task-aware consistency for SSL. The UniTask integrates two auxiliary branches onto a single backbone, each dedicated to performing two types of correlated tasks. Specifically, our network consists of a medical segmentation (MS) branch at the pixel level, a level-set (LS) branch at the geometry level from a strong-correlation perspective, and a point set (PS) branch at the point level from a weak-correlation viewpoint. Consequently, our UniTask, with the incorporation of two additional tasks, facilitates interactions and induces inherent segmentation perturbations at three distinct levels, thereby promoting both supervised and semi-supervised learning. The proposed methods undergo extensive evaluation on inner cell mass (ICM) and left atrium (LA) datasets. Comfortingly, our strategies yield obvious improvements compared with state-of-the-art methods, thus validating the efficacy of our hypothesis.