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Digitalisation is one of the main drivers of most economic sectors nowadays and the digital twin, as a reification of digitalisation for complex systems has attracted much attention from both academics and industry. There have been studies focusing on digital twins in a specific sector while there are few exercising insightful comparisons of digital twins from different domains. Considering the digital twinning is a cross-domain transformation, it is beneficial to establish the principles of universality and variation that can explain similarities and differences in any digital twins. This paper first delivers a comparative analysis of digital twins in five domains through a six-dimensional characterisation framework. Then, by departing from the correlations among the domain-specific DT development, a cross-domain Digital Twin Platform-as-a-Service (DT-PaaS) is proposed to universalise the common process, tools and applications, meanwhile being inclusive of variations of every digital twin instance. As a centralised data, modeling and service platform, it is expected to break the barriers between domains by enabling the cross-domain digital twin data sharing, interoperability and development synergy and tackle some complex global challenges such as climate challenge, net zero, pandemics, etc.