Graph domain adaptation (GDA), which transfers knowledge from a labeled source domain to an unlabeled target graph domain, attracts considerable attention in numerous fields. However, existing methods commonly employ message-passing neural networks (MPNNs) to learn domain-invariant representations by aligning the entire domain distribution, inadvertently neglecting category-level distribution alignment and potentially causing category confusion. To address the problem, we propose an effective framework named Coupling Category Alignment (CoCA) for GDA, which effectively addresses the category alignment issue with theoretical guarantees. CoCA incorporates a graph convolutional network branch and a graph kernel network branch, which explore graph topology in implicit and explicit manners. To mitigate category-level domain shifts, we leverage knowledge from both branches, iteratively filtering highly reliable samples from the target domain using one branch and fine-tuning the other accordingly. Furthermore, with these reliable target domain samples, we incorporate the coupled branches into a holistic contrastive learning framework. This framework includes multi-view contrastive learning to ensure consistent representations across the dual branches, as well as cross-domain contrastive learning to achieve category-level domain consistency. Theoretically, we establish a sharper generalization bound, which ensures the effectiveness of category alignment. Extensive experiments on benchmark datasets validate the superiority of the proposed CoCA compared with baselines.