Video Temporal Grounding (VTG) aims to localize temporal segments in long, untrimmed videos that align with a given natural language query. This task typically comprises two subtasks: \textit{Moment Retrieval (MR)} and \textit{Highlight Detection (HD)}. While recent advances have been progressed by powerful pretrained vision-language models such as CLIP and InternVideo2, existing approaches commonly treat all text tokens uniformly during cross-modal attention, disregarding their distinct semantic roles. To validate the limitations of this approach, we conduct controlled experiments demonstrating that VTG models overly rely on [EOS]-driven global semantics while failing to effectively utilize word-level signals, which limits their ability to achieve fine-grained temporal alignment. Motivated by this limitation, we propose DualGround, a dual-branch architecture that explicitly separates global and local semantics by routing the [EOS] token through a sentence-level path and clustering word tokens into phrase-level units for localized grounding. Our method introduces (1) token-role-aware cross modal interaction strategies that align video features with sentence-level and phrase-level semantics in a structurally disentangled manner, and (2) a joint modeling framework that not only improves global sentence-level alignment but also enhances fine-grained temporal grounding by leveraging structured phrase-aware context. This design allows the model to capture both coarse and localized semantics, enabling more expressive and context-aware video grounding. DualGround achieves state-of-the-art performance on both Moment Retrieval and Highlight Detection tasks across QVHighlights and Charades-STA benchmarks, demonstrating the effectiveness of disentangled semantic modeling in video-language alignment.