A space-air-ground-sea integrated network (SAGSIN) has emerged as a cornerstone of 6G systems, establishing a unified global architecture by integrating multi-domain network resources. Motivated by the demand for real-time situational awareness and intelligent operational maintenance, digital twin (DT) technology was initially regarded as a promising solution, owing to its capability to create virtual replicas and emulate physical system behaviors. However, in the context of SAGSIN, the high-fidelity, full-scale modeling paradigm inherent to conventional DTs encounters fundamental limitations, including prohibitive computational overhead, delayed model synchronization, and cross-system semantic gaps. To address these limitations, this survey paper proposes a novel twinning framework: goal-oriented semantic twin (GOST). Unlike DTs that pursue physical mirroring, GOST prioritizes ``utility'' over ``fidelity,'' leveraging semantic technologies and goal-oriented principles to construct lightweight, task-specific representations. This paper systematically articulates the GOST framework through three layers: knowledge-based semantics, data-driven semantics, and goal-oriented principles. Furthermore, we provide a comprehensive tutorial on constructing GOST by detailing its core enabling technologies and introduce a multidimensional evaluation framework for GOST. We present a case study targeting collaborative tracking tasks in remote satellite-UAV networks, demonstrating that GOST significantly outperforms conventional DTs in timeliness of perceptual data and collaborative tracking. Finally, we outline research directions, establishing GOST as a transformative twinning paradigm to guide the development of SAGSIN.

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