Dense image correspondence is central to many applications, such as visual odometry, 3D reconstruction, object association, and re-identification. Historically, dense correspondence has been tackled separately for wide-baseline scenarios and optical flow estimation, despite the common goal of matching content between two images. In this paper, we develop a Unified Flow \& Matching model (UFM), which is trained on unified data for pixels that are co-visible in both source and target images. UFM uses a simple, generic transformer architecture that directly regresses the $(u,v)$ flow. It is easier to train and more accurate for large flows compared to the typical coarse-to-fine cost volumes in prior work. UFM is 28\% more accurate than state-of-the-art flow methods (Unimatch), while also having 62\% less error and 6.7x faster than dense wide-baseline matchers (RoMa). UFM is the first to demonstrate that unified training can outperform specialized approaches across both domains. This result enables fast, general-purpose correspondence and opens new directions for multi-modal, long-range, and real-time correspondence tasks.