To ensure the secure and stable operation of smart grids, fast and accurate detection of false data injection attacks (FDIA) is critical. Existing data-driven FDIA detection models primarily rely on fixed discrimination thresholds for anomaly identification. However, this approach has notable limitations: attackers can iteratively probe and analyze model responses, gradually adjusting the magnitude of injected attacks to bypass detection, thereby reducing detection accuracy. To address this issue, this paper proposes a FDIA detection model based on correlation discrepancy. First, a detection framework centered on data correlation discrepancies is designed. Second, a position-aware correction factor is embedded to constrain attention scopes, enabling prior correlation extraction with enhanced positional awareness. Then, leveraging the fine-grained and multi-scale characteristics of measurement data sequences, a dual-stream granularity alignment method is developed to capture sequential correlations. Finally, topological correlations are incorporated to define correlation discrepancies, and an adversarial discrimination criterion is formulated through adversarial training to amplify the distinguishability between normal and attacked measurements, resulting in an effective discrimination criterion. Experimental results demonstrate that the proposed model achieves superior detection accuracy and robustness compared with existing methods and performs well under injection attacks of varying magnitudes.