In the coming sixth generation (6G) communication era, to provide seamless and ubiquitous connections, the space-air-ground-sea integrated network (SAGSIN) is envisioned to address the challenges of communication coverage in areas with difficult conditions, such as the forest, desert, and sea. Considering the fundamental limitations of the SAGSIN including large-scale scenarios, highly dynamic channels, and limited device capabilities, traditional communications based on Shannon information theory cannot satisfy the communication demands. Moreover, bit-level reconstruction is usually redundant for many human-to-machine or machine-to-machine applications in the SAGSIN. Therefore, it is imperative to consider high-level communications towards semantics exchange, called semantic communications. In this survey, according to the interpretations of the term "semantics", including "significance", "meaning", and "effectiveness-related information", we review state-of-the-art works on semantic communications from three perspectives, which are 1) significance representation and protection, 2) meaning similarity measurement and meaning enhancement, and 3) ultimate effectiveness and effectiveness yielding. Sequentially, three types of semantic communication systems can be correspondingly introduced, namely the significance-oriented, meaning-oriented, and effectiveness/task-oriented semantic communication systems. Implementation of the above three types of systems in the SAGSIN necessitates a new perception-communication-computing-actuation-integrated paradigm (PCCAIP), where all the available perception, computing, and actuation techniques jointly facilitates significance-oriented sampling & transmission, semantic extraction & reconstruction, and task decision. Finally, we point out some future challenges on semantic communications in the SAGSIN. ...