Trajectory prediction in multi-agent sports scenarios is inherently challenging due to the structural heterogeneity across agent roles (e.g., players vs. ball) and dynamic distribution gaps across different sports domains. Existing unified frameworks often fail to capture these structured distributional shifts, resulting in suboptimal generalization across roles and domains. We propose AdaSports-Traj, an adaptive trajectory modeling framework that explicitly addresses both intra-domain and inter-domain distribution discrepancies in sports. At its core, AdaSports-Traj incorporates a Role- and Domain-Aware Adapter to conditionally adjust latent representations based on agent identity and domain context. Additionally, we introduce a Hierarchical Contrastive Learning objective, which separately supervises role-sensitive and domain-aware representations to encourage disentangled latent structures without introducing optimization conflict. Experiments on three diverse sports datasets, Basketball-U, Football-U, and Soccer-U, demonstrate the effectiveness of our adaptive design, achieving strong performance in both unified and cross-domain trajectory prediction settings.