Illegal, unreported, and unregulated fishing threatens marine ecosystem health and sustainable fisheries management, highlighting the need for reliable fishing-vessel behavior recognition from Automatic Identification System (AIS) trajectories. However, AIS-derived operational states often exhibit overlapping motion patterns, particularly between Underway and Fishing and between Anchored and Moored. This study proposes FishFormer, a local–global spatio-temporal deep learning framework designed for recognizing four AIS-status-derived fishing-vessel operational states: Underway, Fishing, Anchored, and Moored. FishFormer integrates dual-stream spatio-temporal attention, local–global feature fusion, and feed-forward feature enhancement to capture long-range trajectory dependencies, local motion variations, and heterogeneous kinematic features. Experiments on 8139 real-world AIS trajectory segments from U.S. coastal waters show that FishFormer achieves 96.63% overall accuracy and an F1-score of 0.9661. Compared with seven baseline models under a unified experimental protocol, FishFormer shows superior recognition performance, while ablation, confusion-matrix, and robustness analyses further verify the effectiveness of the proposed modules and their contribution to reducing errors among similar behavior states. These results indicate that local–global spatio-temporal learning improves AIS-based operational-state recognition and can provide a behavioral information layer for fishing-vessel activity monitoring and fishery management decision support.