QtSql isn't a database engine like SQLite is, rather it is software for accessing databases through the Qt environment.
The Qt SQLite plugin makes it possible to access SQLite databases. SQLite is an in-process database, which means that it is not necessary to have a database server. SQLite operates on a single file, which must be set as the database name when opening a connection. If the file does not exist, SQLite will try to create it. SQLite also supports in-memory databases, simply pass ":memory:" as the database name. - Source