Visual Anomaly Detection (VAD) is crucial for industrial inspection, yet most existing methods are limited to single-category scenarios, failing to address the multi-class and continual learning demands of real-world environments. While Teacher-Student (TS) architectures are efficient, they remain unexplored for the Continual Setting. To bridge this gap, we propose AdapTS, a unified TS framework designed for multi-class and continual settings, optimized for edge deployment. AdapTS eliminates the need for two different architectures by utilizing a single shared frozen backbone and injecting lightweight trainable adapters into the student pathway. Training is enhanced via a segmentation-guided objective and synthetic Perlin noise, while a prototype-based task identification mechanism dynamically selects adapters at inference with 99\% accuracy. Experiments on MVTec AD and VisA demonstrate that AdapTS matches the performance of existing TS methods across multi-class and continual learning scenarios, while drastically reducing memory overhead. Our lightest variant, AdapTS-S, requires only 8 MB of additional memory, 13x less than STFPM (95 MB), 48x less than RD4AD (360 MB), and 149x less than DeSTSeg (1120 MB), making it a highly scalable solution for edge deployment in complex industrial environments.