Web SQL Database is a SQL-based API allowing a web pages to store and retrieve structured data locally. It is based on, but not the same as SQLite.
Web SQL Database is a SQL-based API allowing web browsers/extensions/apps to store structured data locally. It is based on SQLite and, in practice, has been implemented solely on SQLite.
The API is currently supported by Google Chrome, Opera and Safari. But, The W3C has abandoned Web SQL in favor of Web Storage and the Indexed Database API. From the Web SQL spec:
... specification work has stopped. The specification reached an impasse: all interested implementors have used the same SQL backend (SQLite), but we need multiple independent implementations to proceed along a standardisation path.
Mozilla will not implement Web SQL DB, opting to implement IndexedDB instead, and Microsoft has hinted that they are more likely to implement IndexedDB than Web SQL.