Web 3.0, written with a space and a version number, is most often used today as another spelling of Web3, where the ideas, technologies and criticisms are covered in full. The spelling follows the pattern of Web 1.0 and Web 2.0, presenting the blockchain-based web as the next numbered stage.
In this sense Web 3.0 describes an internet in which users hold their own assets and identities in a Web3 wallet, applications run on public blockchains, and control is spread across networks rather than held by a few platform companies, a goal tied to decentralization. The short form "Web3" was coined in 2014 by Gavin Wood, a co-founder of Ethereum.
The two spellings once meant different things. Before blockchain, "Web 3.0" was used by Tim Berners-Lee and others for the Semantic Web, a vision of web data tagged so that computers could understand and connect it automatically. Some writers still use the term in that older sense, or for a web shaped by artificial intelligence, so the context of a document matters.
In crypto writing the forms are now largely interchangeable, though "Web3" is more common, and some authors reserve "Web 3.0" for the broader, non-blockchain idea of a smarter web.