We present GvSeg, a general video segmentation framework for addressing four different video segmentation tasks (i.e., instance, semantic, panoptic, and exemplar-guided) while maintaining an identical architectural design. Currently, there is a trend towards developing general video segmentation solutions that can be applied across multiple tasks. This streamlines research endeavors and simplifies deployment. However, such a highly homogenized framework in current design, where each element maintains uniformity, could overlook the inherent diversity among different tasks and lead to suboptimal performance. To tackle this, GvSeg: i) provides a holistic disentanglement and modeling for segment targets, thoroughly examining them from the perspective of appearance, position, and shape, and on this basis, ii) reformulates the query initialization, matching and sampling strategies in alignment with the task-specific requirement. These architecture-agnostic innovations empower GvSeg to effectively address each unique task by accommodating the specific properties that characterize them. Extensive experiments on seven gold-standard benchmark datasets demonstrate that GvSeg surpasses all existing specialized/general solutions by a significant margin on four different video segmentation tasks.